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littp://www.arcliive.org/details/foundersmanualprOOpayn 



THE 

FOUNDER'S MANUAL 

A PRESENTATION OF MODERN 
FOUNDRY OPERATIONS 

FOR THE USE OF 

lOUNDRYMEN, FOREMEN, STUDENTS 
AND OTHERS 



BY 

DAVID W. PAYNE 

EDITOR OF "steam" 



245 ILLUSTRATIONS 




NEW YORK 

D. VAN NOSTRAND COMPANY 

25 Park Place 

1917 



t6 



■Tj 



30 



Copyright, 191 7, by 
D. VAN NOSTRAND COMPANY 



in- It 



b 



APR -5 1917 

PRICE, $Jr^O-()....- ™l^ 



©GI.A460168 



PREFACE 

While there is Kttle a foundryman needs to know 
which has not been fully treated by competent authori- 
ties, there is not, so far as I am aware, any summary of 
this great mass of publications. 

In a foundry experience covering many years, I have 
frequently spent hours at a time in searching for special 
information. Believing, therefore, that a compilation of 
this matter, with authoritative instruction for the solu- 
tion of the many problems which are continually pre- 
sented in the foundry, all properly arranged for ready 
reference, would receive a favorable reception, an attempt 
has been made to meet this need by the production of 
this book. 

The material for the Manual has been drawn from 
every available source. The proceedings of the American 
Foundrymen's Association have furnished no end of 
information. The publications of Professors Turner, 
Porter, Reis, Dr. Moldenke, Messrs. Keep, Longmuir, 
Outerbridge, West and others have been most carefully 
searched. Much has been taken from '' The Foundry, '^ 
'' Castings " and '' Iron Age." A great many of the 
" Foundry " records are given in full. 

Possibly, in some cases, special credit for extracts 
has not been accorded; for such omissions indulgence 
is asked, as there has been no intentional neglect or 
lack of courtesy. 

iii 



iv Preface 

In the selection of the material for the book, proper 
consideration has been taken of beginners and others 
who may have not gotten very far in their acquisition 
of foundry information. For such men, it is also hoped 
the book will be of good service. 

As regards the price Ksts and discounts which are 
given in connection with many foundry supplies, it 
should be stated that these are not quoted as current 
prices. They are offered simply as furnishing a guide 
to close approximation of costs. 

The matter for the preHminary portion of the book 
relating to elementary Mathematics, Mechanics, etc., 
has been taken in large part from such authorities as 
Rankine, Bartlett, Wentworth, Trau twine, Kent, Jones 
and Laughlin, Carnegie Steel Co., and the Encyclopedia 
Britannica. 

D. W. P. 

New York, Jan., 1917. 



CONTENTS 



CHAPTER I 

Elementary Mathematics i 

Ratio and Proportion, i. Root of Numbers, 3. Percentage, 
5. Algebra, 7. Equations, 11. Plane Geometry, 15. The 
Parabola, 22. The Hyperbola, 23. Properties of Plane Fig- 
ures, 24. Mensuration, Plane Surfaces, 26. Solids, 30. 

CHAPTER II 

Weights and Measures 35 

Commercial Weights and Measures, 36. Metric Weights and 
Measures, 40. Measures of Work, Power and Duty, 45. 
Mathematical Tables, 46. 

CHAPTER III 

Natural Sines, Tangents, Etc 107 

Solution of the Right-angled Triangle, 109. Solution of Ob- 
lique-angled Triangles, 109. Tables of Sines, Tangents and 
Secants, no. Approximate Measurement of Angles, 115. 
Tapers per foot and Corresponding Angles, 117. 



CHAPTER IV 

Materials 

Wire and Sheet Metal Gauges, 119. Weights of Iron and 
Steel, 122. Cold-rolled Steel Shafting, 140. Galvanized and 
Corrugated Sheet Iron, 141. Sheet Tin, 142. Copper and 
Brass, 143. Metal Fillets, 145. Iron Wire, 146. Nails and 
Tacks, 148. Threads, 149. Bolts, Nuts and Washers, 150. 
Set Screws, 160. Turnbuckles, 162. Cotters, 164. Thumb- 
screws, 165. Rivets, 166. Iron Pipe, 167. Tin and Zinc, 
169. Lead Pipe, 171. Chains and Cables, 173. Sprocket- 
wheels, 176. Modulus of Elasticity, 181. Deflections, 184. 
Modulus of Rupture, 185. Moment of Inertia, 187. Strength 
of Beams, 188. 

V 



119 



vi Contents 

Page 
CHAPTER V 

Mechanics 191 

Acceleration of Falling Bodies, I'gi. Center of Gravity, 194. 
Radius of Gyration, 197. Specific Gravities, 108. Physical 
Constants, 202. Expansion of Solids, 205. Measurement 
of Heat, 207. Radiation of Heat, 208. Equivalent Tem- 
peratures, 211. Strength of Materials, 213. Properties of 
Air, 215. Pressure of Water, 219. Electrical and Mechanical 
Units, 220. 

CHAPTER VI 

Alloys 222 

Alloys of Copper, Tin and Zinc, 222. Aluminum bronze, 226. 
Bearing Metals, 226. 

Belting 227 

Formulas for Width of Belts, 228. Speed of Belts, 229. Rules 
for Speeds and Diameters of Pulleys, 231. Formulas for Cast 
Iron Fittings, 232. 

CHAPTER VII 

Useful Information 234 

Shrinkage of Castings, 234. Window Glass, 236. Fire Clays, 
236. Weight of Metals, 239. Iron Ores, 240. 

CHAPTER VIII 

Iron 241 

Physical Properties of Iron, 241. Grading Pig Iron, 242. 
Standard Specifications for Pig Iron, 246. Machine-cast Pig 
Iron, 248. Charcoal Iron, 250. Grading Scrap Iron, 250. 

CHAPTER IX 

Chemical Constituents of Cast Iron 252 

Influence of Carbon, 252. Loss or Gain of Carbon in Re- 
melting, 254. Influence of Silicon^ 256. Influence of Sulphur, 
260. Influence of Phosphorus, 263. Influence of Manganese, 
265. Aluminum, 266. Nickel, 267. Titanium, 267. Vana- 
dium, 268. Thermit, 270. Oxygen, 270. Nitrogen, 271. 

CHAPTER X 

Mixing Iron 275 

Mixing by Fracture, 273. Mixing Iron by Analysis, 274. 
Castings for Agricultural Machinery, Cylinders and Fly- 
wheels, 277. Castings for Chills, Motor Frames and Gas En- 



Contents vii 

Page 
gines, 278. Castings for Gears, Hydraulic Machinery and 
Locomotives, 280. Castings for Pulleys, Radiators and Heat- 
ers, 284. Castings for Weaving, Woodworking Machinery, 
etc., 287. 

CHAPTER XI 

Steel Scrap in Mixtures of Cast Iron 290 

Recovering and Melting Shot Iron, 291. Burnt Iron, 293. 
Melting Borings and Turnings, 293. 

CHAPTER XII , 

Test Bars 294 

Report of Committee on Test Bars of American Foundry- 
man's Association, 294. Proposed Specifications for Gray 
Iron, 296. Patterns for Test Bars of Cast Iron, 297. Erratic 
Results, 298. Table of Moduli of Rupture, 299. Comparison 
of Test Bars, 302. Casting Defects, 304. Circular Test Bars, 
304. Effect of Structure of Cast Iron Upon its Physical Prop- 
erties, 306. Mechanical Tests, 307. Chemical Analysis, 308. 
Chilled and Unchilled Bars, 310. Forms of Combination of 
Iron and Carbon, 313. 

CHAPTER XIII 

Chemical Analyses 315 

Strength, 315. Elastic Properties, 322. Hardness, 324. 
Grain Structure, 329. Shrinkage, 329. Fusibility, 332. 
Fluidity, 334. Resistance to Heat, 335. Electrical Proper- 
ties, 338. Resistance to Corrosion, 340. Resistance to Wear, 
•342. Coefficient of Friction, 342. Casting Properties, 343. 
Micro-structure of Cast Iron, 345. 

CHAPTER XIV 

Standard Specifications for Cast Iron Car Wheels 350 

Chemical Properties, 350. Drop Tests, 350. Marking, 351. 
Measures, 351. Finish, 351. Material and Chili, 351. In- 
spection and Shipping, 352. Retaping, 353. Thermal Test, 
353. Storing and Shipping, 354. Rejections, 354. 

Standard Specifications for Locomotive Cylinders 355 

Process of Manufacture, 355. Chemical Properties, 355. 
Physical Properties, 355. Test Pieces, 355. Character of 
Castings, 355. Inspector, 355. 



vm Contents 

Page 

Standard Specifications for Cast Iron Pipe 356 

Allowable Variations, 356. Defective Spigots, 357. Special 
Castings, 357. Tables of General Dimensions, 358. Marking, 
360. Quality of Iron, 360. Tests, 361. Cleaning and Coat- 
ing, 361. Contractor, Engineer, Inspector, 362. Tables of 
Weight of Pipe, 364. 

CHAPTER XV 

Mechanical Analysis 371 

Shrinkage Chart, 372. Keep's Strength Table, 375. Stand- 
ard Methods for Determining the Constituents of Cast Iron, 

377- 

CHAPTER XVI 

Malleable Cast Iron 382 

Black Heart, 382. Ordinary or Reaumur Malleable Iron, 385. 
Temperature Curve for Annealing Oven, 386. Analysis Be- 
fore and After Annealing, 387. American Practice, 389. 
. Specifications, 392. Comparison of Tests, 392. 

CHAPTER XVII 

Steel Castings in the Foundry . 1 394 

Normal Steels, 396. Bessemer Process, 396. The Baby Con- 
verter, 397. Annealing, 400. Tropenas Process, 401. Chem- 
istry in the Process, 403. Converter Linings, 404. Standard 
Specifications, 409. Open Hearth Methods, 411. Compara- 
tive Cost of Steel Castings, 417. Basic Open Hearth, 418. 
Acid Open Hearth, 419. Converter, 420. Converter with 
Large Waste, 421. Crucible Castings, 423. Electric Fur- 
nace, 424. 

CHAPTER XVIII 

Foundry Fuels 425 

Anthracite Coal, 425. Coke, 425. By-product Coke, 426. 
Effect of Atmospheric Moisture Upon Coke, 427. Specifica- 
tions for Foundry Coke, 428. Fluxes, 429. Comparison of 
Slags, 432. Fire Brick and Fire Clay, 434. Fire Sand, 435. 
Magnesite, 436. Bauxite, 436. 

CHAPTER XIX 

The Cupola 437 

The Lining, 437. Tuyeres, 439. The Breast, 440. Sand 
Bottom, 441. Zones of Cupola, 442. Chemical Reaction in 



Contents ix 

Page 
Cupola, 443. Wind box, 445. The Blast, 446. Sturtevant 
Blowers, 448. Buffalo Blowers, 449. Root Blowers, 449. 
Diameter of Blast Pipe, 450. Dimensions of Cupolas, 451. 
Charging and Melting, 452. The Charging Floor, 453. Melt- 
ing Losses, 454. Melting Ratio, 461. Appliances About 
Cupola, 462. Ladles, 462. Tapping Bar, 463. Bod Stick, 
463. Capacities of Ladles, 464. Applying Metalloids in La- 
dles, 465. Cranes, 466. Spill Bed, 466. Gagger Moulds, 467. 

CHAPTER XX 

Moulding Sand 468 

Bonding Power, 468. Permeability and Porosity, 468. Re- 
fractoriness, 469. Durability, 469. Texture, 469. Grades, 
470. Sandfor Brass, 472. Testing Sand, 473. For Dry Sand 
Moulding, 477. Skin Drying, 469. Core Sand, 479. Core 
Mixtures, 480. Dry Binders, 481. Parting Sand, 486. 
Facings, 486. 

CHAPTER XXI 

The Core Room and Appurtenances 492 

Core Oven Carriages, 496. Mixing Machines, 497. Sand 
Conveyors, 497. Rod Straighteners, 497. Wire Cutter, 497. 
Sand Driers, 498. Core Plates, 498. Core Machines, 499. 
Cranes and Hoists, 499. 

CHAPTER XXII 

The Moulding Room 501 

Cranes, 502. Hooks, Slings and Chains, 502. Lifting Beams, 
503. Safe Loads, 504. Binder Bars, 505. Clamps, 506. 
Flasks, 506. Iron Flasks, 510. Sterling Steel Flasks, 515. ^ 
Snap Flasks, 517. Slip Boxes, 519. Pins, Plates and Hinges, 
519. Sweeps, 522. Anchors, Gaggers and Soldiers, 523. 
Sprues, Risers and Gates, 524. Top Pouring Gates, 526. 
Whirl Gates, 527. Skim Gates, 527. Horn Gates,' 527. 
Strainers and Spindles, 528. Weights, 528. Chaplets, 528. 
Liquid Pressure on Moulds, 529. Nails, 536. Sprue Cutters, 
537- 

CHAPTER XXIII 

Moulding Machines 538 

Jigs, 540. Flasks, 547. Moulding Operations, 549. 



X Contents 

Page 
CHAPTER XXIV 

Continuous Melting 551 

Multiple Moulds, 555. Permanent Moulds, 558. Centrif- 
ugal Castings, 561. Castings Under Pressure, 562. Direct 
Casting, 562. Carpenter Shop and Tool Room, 562. The 
Cleaning Room, 563. Tumbling Mills, 563. Chipping, 566. 
Grinding, 566. Sand Blast, 566. Pickling, 567. 

CHAPTER XXV 

Determination of Weight of Castings ... , 569 

By Weight of Patterns, 569. Weight of Pattern Lumber, 569. 
Formulas for Finding Weight of Castings, 570. Formulas 
for Weight on Cope, 575. 

CHAPTER XXVI 

Water, Lighting, Heating and Ventilation 577 

Water Supply, 577. Lighting, 578. Heating and Ventila- 
tion, 579. 

CHAPTER XXVII 

Foundry Accounts 587 

Foundry Requisition, 588. Pattern Card, 589. Pig Iron 
Card, 590. Core Card, 591. Heat Book, 592. Cleaning 
Room Report, 597. Weekly Foundry Report, 600. Monthly 
Expenditure of Supplies, 601. Comparison of Accounts, 605. 
Transmission of Orders, 611. American Foimdrymen's As- 
sociation Methods, 612. Cost of Metal, 617. Moulding, 619. 
Cleaning and Tumbling, 620. Pickling, 621. Sand Blast- 
ing, 622. Core Making, 623. A Successful Foundry Cost 
System, 625. Castings Returned, 629. 

CHAPTER XXVIII 

Pig Iron Directory 633 

Classification and Grades of Foundry Iron, 633. Coke and 
Anthracite Irons, 635. Charcoal Irons, 655. 

Authorities 66c 

Index 663 



Most readers of this book will, without doubt, be familiar with the 
ordinary mathematical processes; to them, such brief references as may- 
appear, will, perhaps, seem superfluous. There may be, however, those 
who, from disuse or otherwise, are not so circumstanced. For their 
convenience such information will be given as may facilitate the inter- 
pretation of the formulas and calculations herein. 



SIGNS AND ABBREVIATIONS 



A prime mark ' above a nimiber 
means minutes or linear feet; 
as lo' means ten minutes or ten 
linear feet. 

Two prime marks " likewise mean 
seconds; or linear inches; as lo" 
indicates lo seconds or lo linear 
inches. 

The sign D means square, as D' 
square foot, D " square inch. 

The sign O means round or cir- 
cular, as O" circvilar inch. 

The sign / means an angle. 

The sign L means a right angle. 

The sign -L means a perpendicular. 

The sign x, called Pi, means the 
ratio of the circumference of a 
circle to the diameter, and is 
equal to 3. 141 59. 

The sign g means acceleration due 
to gravity and equals 32.16 foot 
pounds per second. 



The sign E indicates the coefl&cient 

of elasticity. 
The sign / indicates the coefl&cient 

of friction. 
The sign M indicates modulus of 

rupture. 
The sign log indicates the common 

logarithm. 
The sign log e ) hyperbolic 
or log hyp. \ logarithm. 
R.p.m. revolutions per minute. 
H.P. horse power. 
K.W. Hr. Kilowatt hours. 
A.W.G. American wire gauge. 
B.W.G. Birmingham wire gauge. 
A.S.M.E. American Society of 

Mechanical Engineers. 
A.F.A. American Foundrymen's 

Association. 
B.F. A. Birmingham Foundry- 
men's Association. 
I.S.I. Iron and Steel Institute. 



FOUNDERS MANUAL 

ELEMENTARY MATHEMATICS 



CHAPTER I 
SECTION I 
ARITHMETIC 

It is deemed unnecessary to present anything under this branch of 
mathematics, except Ratio and Proportion, Square and Cube Roots, 
Alligation and Percentage. These operations are applied so frequently 
in the foundry that, it is believed, a simple explanation of them will not 
be out of place. 

Ratio and Proportion 

The ratio of two numbers is the relation which the first bears to the 
second and is equivalent to a fraction obtained by dividing the first 
number by the second. 

Thus: S : 7 = f or 7:5 = 1- 

When the first of four numbers is the same fraction of the second, as 
the third is of the fourth, the first has the same ratio to the second as the 
third has to the fourth, and the four numbers are in proportion. Pro- 
portion, therefore, is the equality of two ratios. 

Thus: 

t = T3 = I- 

The proportion is expressed, 4 : 6 :: lo : 15, and is read, 4 is to 6 as 10 
• is to 15. The first and fourth terms are called the extremes; the second 
and third the means. 

The product of the extremes is equal to the product of the means; 
thus in the above proportion 4 X 15 = 6 X 10 = 60. Hence where 
three terms of the proportion are known the fourth can be found. 



2 Arithmetic 

Thus: Find the number to which lo bears the same ratio as 4 does to 6. 
4 : 6 :: 10 : required number. 

Required number equals -\°- =15. 

Where one extreme and both means are known, to find the other 
extreme, divide the product of the means by the known extreme. 

Where both extremes and one mean are known, to find the other mean, 
divide the product of the extremes by the known mean. 

For the purpose of illustrating these rules replace the figures in a 
proportion, by the letters A, B, C, D, and write A : B :: C : D; then, 

AD-BC,^--^,A-—,D--j-,B-—,C.-—. 

To state the terms ot a simple proportion where three are given; 
place that as the third term which is of the same kind as the required 
term; then consider whether the required term should be greater or less 
than the third term; if greater, make the greater of the two remaining 
terms the second and the other the first term. But if the required term 
should be less than the third term, place the smaller of the first two as 
the second term and the greater as the first. 

Thus: What is the price, per net ton, of pig iron sold at $17.50 gross 
ton? 

As the price is required, $17.50 becomes the third term. Since the 
net price is less than the gross, 2000 is the second term and 2240 the first. 
The proportion is then written: 

2240 : 2000 :: $17.50 : answer. 



2000 X $17.50 
2240 



$15.62 = required price. 



Therefore, the net 
price is equal to the gross multiplied by 0.892 +; or $17.50 X .892 = 
$15.62; or the net price being known the gross is equal to the net multi- 



Compound Proportion 

Where the ratio of two quantities depends upon a combination of 
other ratios, the proportion becomes a compound proportion. In this 
as in simple proportion, there is but one third term, and it is of the same 
kind as the required term; there may be two or more first and second 
terms. Set down the third term as in simple proportion; consider each 
pair of terms of the same kind separately and as terms of a simple pro- 
portion, and arrange them in the same manner, making the greater of 



Roots of Numbers 3 

the pair the second term, if the answer considered with reference to this 
pair alone should be greater than the tishd term; or the reverse if it 
should be less. 

Set down the terms under each other in their order of first and second 
terms. Multiply the product of all the second terms by the third term 
and divide this product by that of all the first terms. 

Example. — If 36 men working 10 hours per day perform | of a piece 
of work in 17 days, how long must 25 men work daily to complete the 
work in 16 days? 

The length of the day will be greater the fewer the men, and the fewer 
the days are; and less, the less the work is; hence, the above problem 
is stated as follows: 

Men 25 : 36 :: 10 

Days 16 : 17 :: 

Fifths of work 3 : 2 

36 X 17 X 2 X 10 
25 X 16 X 3 



5J. = 10.2 hours per day. 



Roots of Numbers 

To Extract the Square Root of a Given Number 

Point off the nuniber into periods of two figures each, beginning with 
units; if there are decimals, begin at the decimal point, separating the 
whole number to the left and the decimal to the right into such periods, 
supplying as many ciphers in groups of two, as may be desired. 

Find the greatest number whose square is less than the first left hand 
period and place this to the right of the given nimiber as the first figure 
of the root. Subtract its square from the first left hand period and to 
the remainder annex the second period for a dividend. 

Place before this as a partial divisor, double the root figure just found. 
Find how many times the dividend, exclusive of its right hand figure, 
contains the divisor, and place the quotient as the second figure of the 
root, and also at the right of the partial divisor. 

Multiply the divisor thus completed, by the second root figure and 
subtract the product from the dividend. To this remainder annex the 
next period for a new dividend, and double the two root figures for a 
new partial divisor. Proceed as before until all the periods have been 
brought down. 



Arithmetic 

Example. — Extract the square root of 7840.2752 -f. 

78'40.27'52/88.S453 
64 



168)1440 
1344 



1765)9627 
8825 



17704)80252 
70816 



77085)943600 
885425 



1770903)5817500 
5312709 

To Extract the Square Root of a Fraction 
Find the roots of the numerator and denominator separately; or 
reduce to a decimal and take its root. 

Example.— y ^ = — ^ = ^ ; or ^ = 0.5625, V0.5625 = 0.75. 

To Extract the Cube Root of a Number 
Beginning at the right, point off the number into periods of three 
figures each. If there are decimals, begin at the decimal point, separate 
the whole number to the left, and the decimal at the right into such 
periods; find the greatest cube contained in the left-hand period, and 
write its root as the first figure of the root required. 

Subtract the cube of the first root figure from the left-hand period, 
and to the remainder annex the next period for a dividend. Then 
multiply the square of the first figure of the root by 300 and use the prod- 
uct as a trial divisor; write the quotient as the second root figure. 
Complete the trial divisor by adding to it 30 times the product of the 
first root figure by the second, and the square of the second; multiply 
the completed divisor by the second root figure and subtract the product 
from the dividend. To the remainder annex the next period and proceed 
as before, to find the third figure of the root, i.e., square the first two 
figures of the root and multiply by 300 for a trial divisor. To this add 
30 times the product of the first two root figures by the third, and the 
square of the third for the completed divisor, etc. 

The cube root will always contain as many figures as there are periods 
in the given number. 



Percentage 

Example. — Extract the cube root of 7^-402^ 752 

78'402'752/428. 
64 



4^ X 300 = 4800 14402 
4 X 2 X 30 = 240 
4 



5044 10088 



422 X 300 = 529200 4314752 

42 X 8 X 30 = 10080 
82 = 64 



539344 4314752 



Alligation 

Alligation is the process of determining the value of a mixture of 
different substances, when the quantity and value of each substance 
is known. 

Rule. — Take the sum of all the products of the quantity of each 
substance by its respective price, and divide it by the total quantity; 
the result is the value of one unit of the mixture. 

Example. — What is the value per ton of a mixture containing 500 lbs. 
of pig iron at $18.00 per ton, 275 lbs. at $16.50 and 800 lbs. of scrap at 
$14.00? 

500 X 18 = 9000 

275 X 16.5 = 4537-50 

800 X 14 = 11200.00 



i57S 24737-50 

— = $15,706 per ton. 

1575 

Percentage 
Per cent means so many parts of 100, and is expressed decimally 
as three per cent .03, meaning jf q; one-fourth of one per cent .0025 = 
ToVoo- 

Percentage covers the operations of finding the part of a given 
number at a given rate per cent; as 6 per cent of 2750, 2750 X .06 = 
165.00; of finding what per cent one number is of another as:. What 
per cent of 780 is 39? 

39 ^ 780 = .05 per cent; 
of ascertaining a number when an amount is given, which is a given 
per cent of that number; as 62.5 is .04 per cent of what nimiber? 
62.5 -^ .04 = 1562.5. 



Arithmetic 





Decimal Equivalents of Parts of One Inch 




1-64 


.015625 


17-64 


.265625 


33-64 


.515625 


49-64 


.576625 


1-32 


.031250 


9-32 


.281250 


17-32 


.531250 


25-32 


.781250 


3-64 


.046875 


19-64 


.296875 


35-64 


.546875 


51-64 


.796875 


I-I6 


.062500 


S-16 


.312500 


9-16 


.562500 


13-16 


.812500 


5-64 


.078125 


21-64 


.328125 


37-64 


.578125 


53-64 


.828125 


3-32 


.093750 


11-32 


.343750 


19-32 


.593750 


27-32 


.843750 


7-64 


.109375 


23-64 


.359375 


39-64 


.609375 


55-64 


.859375 


1-8 


.125000 


3-8 


.375000 


5-8 


. 625000 


7-8 


.875000 


^ 9-64 


.140625 


25-64 


.390625 


41-^4 


.640625 


57-64 


.890625 


5-32 


. 156250 


13-32 


.406250 


21-32 


.656250 


29-32 


.906250 


11-64 


.171875 


27-64 


.421875 


43-64 


.671875 


59-64 


.921875 


3-16 


. 187500 


7-16 


.437500 


11-16 


.687500 


IS-16 


.937500. 


13-64 


.203125 


29-64 


.453125 


45-64 


.703125 


61-64 


.953125 


7-32 


.218750 


15-32 


.468750 


23-32 


.718750 


31-32 


.968750 


15-64 


.234375 


31-64 


.484375 


47-64 


.734375 


63-64 


.984375 


1-4 


.250000 


1-2 


.500000 


3-4 


.750000 


I 


I 









Inches to 


Decimals 


OF A 


Foot 















I 


2 


3 


4 


5 


6 


7 


8 


9 


10 


II 






.0833 


.1667 


.2500 


.3333 


.4167 


.5000 


•5833 


.6667 


• 7500 


• 8333 


.9167 


3^1 


.0026 


.0859 


.1693 


.2526 


.3359 


.4193 


.5026 


•5859 


• 6693 


.7526 


.8359 


.9193 


X^B 


.0052 


.0885 


.1719 


.2552 


.3385 


.4219 


• 5052 


•5885 


.6719 


• 7552 


.8385 


.9219 


3% 


.0078 


.0911 


• 1745 


.2578 


.3411 


• 4245 


.5078 


.5911 


• 6745 


• 7578 


.8411 


• 924s 


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Algebra 
Products of Fractions Expressed in Decimals 






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SECTION II 
ALGEBRA 

In algebra quantities of every kind are denoted by letters of the 
alphabet. . 

The first letters of the alphabet are used to denote known quantities, 
and the last letters unknown quantities. 

The sign + (plus) denotes that the quantity before which it is placed 
is to be added to some other quantity. Thus: a + b denotes the sum 
of a and b. 

The sign — (minus) denotes that the quantity before which it is 
placed is to be subtracted from some other quantity. Thus: a — b 
denotes that b is to be subtracted from a. 

When no sign is prefixed to a quantity, + is always understood. 

Quantities are said to have like or unlike signs, according as their 
signs are like or unlike. 



8 Algebra 

A quantity which consists of one term is said to be simple; but if it 
consists of several terms connected by the signs + or — , it is said to be 
compound. Thus: a or — b are simple quantities; but — a — & is a 
compound quantity. 

Addition of Like Quantities 

Add together the coefi&cients of the quantities having like signs, and 
subtract the negative sum from the positive. Thus: Add 7 a -\- 2 Oy 
2, a — a, and 6 a — 4 a. 

y a — a 

2 a — 4a 

3^ 
6 a 



18 a — 5 a = 13 a. 

Addition of Unlike Quantities 

If some of the quantities are unlike, proceed as before with each like 
'quantity, and write down the algebraic sum of all the quantities. Thus: 
Add 7a-\-2b, ^a — b,6b — 4a and 5^ — 46. 

y a — 4a 2b — b 
S a — 6b — 4b 

5a 

1$ a — 4a 86 — 56 
— 4a — 5& 

II a 36 

Answer = 11 a + 3 J. 

The process is the same with compound quantities. Thus: Add 
a^b + 2 cd^ to - 2 a?b + cJ^ = 3 c(P - a^b. 

Subtraction 

Change the sign of the subtrahend and proceed as in addition. Thus: 
Subtract ^ a^b — g c from 4 a^b + c; changing the signs of the subtra- 
hend and adding, the expressions may be written 

4a^b — ^a^b -\- c-\- gc or a^b + 10 c. 

Multiplication 

If the quantities to be multiplied have like signs, the sign of the 
product is + ; if they have unlike signs, that of the product is — . 



Powers of Quantities g 

Of Simple Quantities 

Multiply the coefficients together and prefix the + or — sign, accord- 
ing as the signs of the quantities are like or unlike. Thus: 
Multiply -\- ahy -\- b. Product equals -f- ab. 
Multiply + 5 5 by — 4 c. Product equals — 20 be. 
Multiply — ^axhy -\- yab. Product equals — 21 a^x. 

Of Compound Quantities 

Multiply each term of the multiplicand by all the terms of the multi- 
plier, one after the other as by former rule; collect their products into 
one sum for the required product. 
Example. — 

Multiply a — b + c 
by a + b — c 





a^ — /lifS -\- flc 






+ aif 


- 62 + he 




— a-c 


+ be -c^ 




a^ 


-b^ + 2be- c^ 


Multiply 


2X+ y 




by 


X — 2 y 





2x^ -\- xy 

— 4 xy — 2 y^ 

20^— TyXy— 2'f 

Powers of Quantities 

The products arising from the continued multiplication of the same 
quantity by itself are called powers of that quantity; and the quantity 
itself is called the root. 

The product of two or more powers of any quantity is the quantity 
with an exponent equal to the sum of the exponents of the powers. 

Thus: 

a2 X a^ = flS. fl2j X aJ = aW\ 4 a6 X — 3 ac = — i.2a^be. 

The square of the sum of two quantities equals the sum of their 
squares plus twice their product. 

{a + 6)2 = a2 + 62 + 2 ab. 

The square of the difference of two quantities is the sum of their 
squares minus twice their product. 

(a - 6)2 = a2 + 62 - 2 ab. 



10 Algebra 

The product of the sum and difference of two quantities is equal to 
the difference of their squares. 

(a + b) (a-b) =0"- ¥. 

The squares of half the sum of two quantities is equal to their product 
plus the square of half their difference. 

Thus: ia + hY , , {a - h^ 

= ab -] 

2 2 

The square of a trinomial is equal to the sum of the squares of each 

term plus twice the product of each term by each of its following terms- 

Thus: {a + b + cy = a^ + b^ + c^ + 2ab-\-2ac-\-2bc. 

(a — b — cf = a^ -\- b^ -{- c^ — 2 ab — 2 ac -{- 2 be. 

Parenthesis ( ) 

When a parenthesis is preceded by a plus sign, it may be removed 
without changing the value of the expression. 

Thus: {a + b)-}-(a + b) = 2a+2b. 

But if preceded by a minus sign,' if removed, the signs of all the terms 
within the parenthesis must be changed. 

Thus: (a + b) — {a — b)=a + b — a + b = 2b. 

When a parenthesis is within a parenthesis, remove the inner one first. 

Thus: a-[b-[c-{d- e)]] = a - [b - [c - d + e]] = 

a — [b — c + d — e] = a — b + c — d -{- e. 

Where the sign of multiplication ( X ) appears, the operation indicated 
by it must be performed before that of addition or subtraction. 

Division 

If the sign of the divisor and dividend be like, the sign of the quotient 
is plus (+); but if they be unlike the sign of the quotient is minus (— ). 

To Divide a Monomial by a Monomial 

Write the dividend over the divisor with a line between them. If the 
expressions have common factors remove them. 

Thus: ,, , a^bx ax a^ 1 „ 

a^x -V- aby = —r— = — ;i = "i = ^~ 
aby y a^ a^ 

To Divide a Polynomial by a Monomial 

Divide each term of the polynomial by the monomial. 
Thus: (8 a6 — 12 ac) 4- 4 a = 2 6 — 3 c. 



Simple Equations ii 

To Divide a Polynomial by a Polynomial 

Arrange the terms of both dividend and divisor according to the as- 
cending or descending powers of some letter, and keep this arrangement 
throughout the operation. Divide the first term of the dividend by 
the first term of the divisor, and write the result as the first term of the 
quotient. 

Multiply all the terms of the divisor by the first term of the quotient 
and subtract the product from the dividend. If there is a remainder 
consider it as a new dividend and proceed as before. 

Thus: 



{a' - b') 


-^ia + b) 


a + b)a^ 


-b\a 


-b 


a^ 


+ ab 






-ab- 


-62 




-ab- 


-62 



(i) The difference between two equal powers of the same quantities 
is divisible by their difference. 

(2) The difference between two equal even powers of the same quan- 
tities is divisible by their sum or difference. 

(3) The sum of two equal even powers of the same quantities is not 
divisible by their sum or difference. 

(4) The sum of two equal odd powers of the same quantities is 
divisible by their sum, 

(5) The sum of two equal even powers, whose exponents are composed 
of odd and even factors, is divisible by the sum of the powers of the 
quantities expressed by the even factor. 

Thus: {x^ + y) is divisible by (x^ + y^). 



Simple Equations 

An equation is a statement of equahty between two expressions; as 
a-\-b = c -{- d. 

A simple equation, or equation of the first degree, is one which contains 
only the first power of the unknown quantity. 

If both sides of the equation be changed equally, by addition, sub- 
traction, multiplication or division, the equality will not be disturbed. 

Any term of an equation may be changed from one side to the other 
provided its sign be changed. 

Thus: a-]-b = c-{-d, a = c + d — b. 



1^ Algebra 

To Solve an Equation Having One Unknown Quantity 

Transpose all the terms containing the unknown quantity to one side 
of the equation, and aU the other terms to the other side. 

Combine like terms, and divide both sides by the coefi&cient of the 
unknown quantity. 

Thus: 8 .T — 29 = 26 — 3 X, 11 a; = 55, a; = 5. 

Simple algebraic problems containing one unknown quantity, are 
solved by making x equal the unknown quantity, and stating the con- 
ditions of the problem in the form of an algebraic equation, then solving 
the equation. 

Thus : What two nmnbers are those whose sum is 48 and difference 14? 



Let 


X = the smaller nmnber. 


Then 


a? -1- 14 = the greater number. 




ic + a; + 14 = 48, 




2x = 2>A- 


Therefore 


x= IT, 


and 


a; + 14 = 31, 




31 + 17 = 48. 



Find the number whose treble exceeds 50 by as much as its double 
falls short of 40. 

Let X = the number. 

Then 3 a; — 50 = 40 — 2 x, 

5 a; = 90, X = 18. 

Equations Containing Two Unknown Quantities 

If one equation contains two unknown quantities, an indefinite number 
of pairs of values for them may be found, which will satisfy the equation; 
but if a second equation be given, only one pair of values can be found 
that will satisfy both equations. Simultaneous equations, or those 
which may be satisfied by the same values of the unknown quantity, 
are solved by combining the equations so as to obtain a single equation 
containing only one unknown quantity. 

This process is called elimination. 

Elimination by Addition or Subtraction 

Multiply the equations by such a number as will make the coefficients 
of one of the unknown quantities equal in both. Add or subtract 
according as they have like or unlike signs. 



Elimination by Comparison 13 



Solve 2x-\- sy = 7 

4X- 5y= 3 

Multiply by 2 4^ + 6 y = 14 

Subtract 4-^— 5 y = 3 



II y = II 
y = ^^ 
Substituting the value of y in the first equation 

2X -\- $ = 7, .'. X = 2. 

Elimination by Substitution 

From one of the equations obtain the value of one of the unknown 
quantities in terms of the other. Substitute this value of this imknown 
quantity for it, in the other equation, and reduce the resulting equations. 

Solve . 2 a: + 3 y = 8 (i) 

3 X + 7 y = 7 (2) 

From (i) x = ^~^^ 

2 

Substituting this value in (2) 

(8 — ^ y) 
3- — -^ 1-73' = 7, 24-93;+ i4y= 14, .••y=--2. 

Substituting this value in (i); 

2 a; — 6 = 8, :. x = 7. 

Elimination by Comparison 

From each equation obtain the value of one of the unknown quantities, 
in terms of the other. Form an equation from these equal values of the 
same unknown quantity and reduce. 

Solve 2a; — gy = II (i) 

3^-4^= 7 (2) 

From (i) x = =^^ 

2 

From (2) X = ^-^^l^ 

3 
Placing the values of i»; in a new equation 

ii + gy 7 + 4y 

— ^= ^ , 19^=- 19, .-. y=-i. 

Substituting this value of 3; in (i) 

2« + 9 = II, .'. X = I. 



14 Algebra 

If three simultaneous equations are given containing three unknown 
quantities, one of the unknown quantities must be eliminated between 
two pairs of the equations, then a- second between the two resulting 
equations. 

Quadratic Equations or Equations of the Second Degree 

A quadratic equation contains the square of the unknown quantity, 
but no higher power. A pure quadratic contains the square only; an 
adfected quadratic contains both the square and the first power. 

To Solve a Pure Quadratic * 

Collect the unknown quantities on one side, and the known quantities 
on the other; divide by the coefficient of the unknown quantity and 
extract the square root of each side of the resulting equation. 

Solve 3 ^c^ — 15 = o. _ 

Sx- = 15, .'. x^ = s, x = V5. 

A root which is indicated, but can only be found approximately is 
called a surd. 

Solve 3 a;2 + 15 = o. 

3 a;2 = — 15, x^ = - 5, .'. X = V- 5. 

The square root of a negative quantity cannot be found even approxi- 
mately, for the square of any number is positive; therefore, a root which 
is indicated, but cannot be found approximately is called imaginary. 

To Solve an Adfected Quadratic 

First. — Carry all the terms involving the unknown quantities to one 
side of the equation and the known quantities to the other side. Arrange 
the unknown quantities in the order of their exponents, changing the 
signs of the equation if necessary, so that the sign of the term containing 
the square of the unknown quantity shall be positive. 

Second. — Divide both terms by the coefficient of the square of the 
unknown quantity. 

Third. — To complete the square. 

Add to both sides of the equation, the square of half the coefficient 
of the unknown quantity. The side containing the unknown quantity 
will now be a perfect square. 

Fourth. — Extract the square root of both sides of the equation and 
solve the resulting simple equation. 

Example. — a;^ + 2 a: = 35. 

Add the square of half the coefficient of x, which is i, to both sides; 
then x^ + 2 x -\- 1 = $s + ^ = 3^' 



Plane Geometry 15 

Extracting the square root 

x + i = V^ = rb 6 

X = 6 - 1 = s 

x=— 6 — i = — y. 
Example: 3 rc^ — 4^ = 32. 
Divide by the coefficient of x^ 

x^-^ = ^. 
3 3 

Add the square of half the coefficient of x, which equals {^Y = f ; 
then ^2_|^ + i=3_2_|.4, 

Extracting the square root, the equation becomes 
x-i = VI^ = V- 
^ = ¥ + f = 4, or X = - -1/ + I = - f = - 2f. 

Since the square of a quantity has two roots =t, a quadratic equation 
has apparently two solutions. Both solutions may be correct; but in 
some cases one may be correct and the other inconsistent with the con- 
ditions of the problem. 

For the solution of quadratic equations containing two unknown 
quantities, or for that of equations of a higher order, a more extended 
treatment of the subject is required, than is permissible in a book of this 
character. 

SECTION III 

PLANE GEOMETRY 

Problem 1 

To Bisect a Straight Line, or an Arc of a Circle 

With any radius greater than half AB and with 
A and B as centers, describe arcs cutting each other 
at C and D. Draw the hne CD, which will bisect 
the straight line at E and the arc at F. 



Problem 2 

To Draw a Perpendicular to a Straight Line, or a Radial Line to the Arc 
of a Circle 
This is the same as Problem i, Fig. i. 
CD is perpendicular to AB, ox is radial to the arc. 




l6 Plane Geometry 



Problem 3 

To Draw a Ferpendicular to a Straight Line, from a Given Point on that 

Line 



KXi 



Fig. 2. 



With any convenient radius and the given point C, 
as a center, cut the line AB, at A and B. Then 
with a radius longer than AC, describe arcs from A 
and B intersecting each other at D and E. Draw 
DC, perpendicular to AB. 



In laying out work on the ground or in places where the straight edge 
and dividers are inapplicable: 

Set off six feet from A to B. Then with ^, as a cen- S 

ter and AC = 2>' taken on a tape hne, describe an arc at / 

C; with B, as a center and a radius BC = lo', cut the / 

other arc at C. A line through CA, will be perpendicu- ^/- 'a. 

IsiT to AB. 3, 4 and 5 may be used instead of 6, 8 and ^ 

10; or any multiples of 6, 8, 10 will serve. 



Problem 4 

From a Point at the End of a Given Line to Draw a Perpendicular 



From any point C, above the line, with the radius 
AC, describe an arc, cutting the given line at B. 
Draw BC, and prolong until it intersects the arc at D. 
Then, DA will be perpendicular to AB,ait A. 




Fig. 4. 



Problem 5 



From Any Point Without a Given Straight Line, to Draw a Perpendicular 
to the Line 

Let BC, be the given line; then from any point A, 
with any radius AB, describe arcs cutting the line at y 
B and C. From B and C as centers and any radius ^ 
greater than half of BC, describe arcs intersecting at :1:d 

D. Draw AD, perpendicular to BC. (Fig. 5.) Fjg. 5. 



Plane Geometry 



17 



Fig. 6. 



ProblemTB 

To Draw a Straight Line Parallel to a Given Line at a Given Distance 
from That Line 

D r> 

From any two points on the given line as - 

centers and the given distance as a radius, 
describe the arcs B and D. Draw BD parallel 
to AC. (Fig. 6.) 

Problem 7 
To Divide a Given Straight Line into Any Nunber of Equal Parts 

Let AB he the given Hne. Draw any 
— c Hne AC, intersecting the given line and lay 
off on it, say, 5 equal parts. Join the last 
point 5 with B. Then through each of the 
other divisions on AC, draw lines parallel to 



Fig. 7. 



B 5, dividing AB into 5 equal parts. (Fig. 7.) 



4^ 




Problem 8 

To Draw an Angle of 60°, also One of 30° 

From A with any radius describe the arc CB, then 
with the same radius and B, as a center, cut the arc at 
C. Then the angle CAB = 60°. 

From C drop CD perpendicular to AB. The angle 
ACD = 30^ 

Problem 9 

To Draw an Angle of 45° 



Draw BC, perpendicular to AB. Make BC = AB, 
and draw AC. The angle CAB = 45°. (Fig. 9.) 



Fig. 8. 




Fig. 9- 

Problem 10 

To Bisect an Angle 

Let ABC be the given angle. With 5 as a center and 
any radius, draw the arc AC. Then with A and C as 
centers and a radius greater than one-half AC, describe 
arcs cutting each other at D. Draw BD, which will 
bisect the angle ABC. (Fig. 10.) 



::D 



Fig. 10. 




l8 Plane Geometry 

Problem 11 

Through Two Given Points and With a Given Radius Describe the Arc 
of a Circle 

Referring to Fig. lo. Let A and C be the given points and a distance 
AB the given radius. 

From A and C, with ^5 as a radius describe arcs cutting each other 
at B, then with 5 as a center strike AC. 

All Angles in a semicircle are Right Angles. 

Problem 12 

An Angle at the Center of a Circle is Twice the Angle at the Circumference 
when Both Stand on the same Arc 



P Thus the angle BAC is equal to twice the angle 
BDC. (Fig. II.) 



Problem 13 

All the Angles Between an Arc and its Chord, the Sides of the Angle Pass- 
ing Through the Extremities of the Chord, are Equal. (Fig, 12.) 

h 

F 




Thus, the angle EFG = EEC. 

Fig. 12. 
Problem 14 

To Find the Center of a Circle or of an Arc. (Fig. 13.) 

Take any three convenient points on the circum- 
ference, and with any radius greater than half the 
distance between any two points, describe arcs cut- 
ting each other at d, e, f and g. Through d, f and 
e, g, draw the Hues df and eg; the center is at their 
Fig. 13. intersection H. 

Problem 15 

To Pass a Circle Through Three Given Points 
Referring to Problem 14, let a, h and c be the three given points. 
Proceed in the same way as to find the center H. 




Plane Geometry 



19 



Problem 16 

To Describe an Arc of a Circle Passing Through Three Given Points 
when the Center is not Accessible. (Fig. 14.) 

Let A , B and C be the three given points. 

From A and B as centers and with yl5 as a radius, describe the arcs 
AEdiudBD. 

Draw AD and BE through C Lay off on 
the arc AE, any number of equal parts 
above E and on BD, the same number be- 
low D, numbering the points i, 2, 3, etc., in 
the order in which they are taken. Draw 
from A, lines through i, 2, 3, etc., on the 
arc BD; and from B, lines through i, 2, 3, 
etc., on the arc AE. The intersections of 
lines having corresponding numbers will be points on the required arc 
between C and B. 

Proceed in the same manner to find points between C and A . Then 
draw the arc through the points. 




Fig. 14. 



Problem 17 

From a Point on the Circumference of a Circle Draw a Tangent to 
the Circle. (Fig. 15.) 



Through the given point A draw the radial line 
AC. Then on ^C erect the perpendicular BE, as 
in Problem 3. 




Fig. 15. 

Problem 18 

From a Point Without a Circle Draw a Tangent to the Circle. (Fig. 16.) 



Let A be the center of the circle, and B the 
given point. Join A and B, and on the hne AB 
describe a semicircle, with a radius equal to one- 
half oi AB. Through the intersection of the 
semicircle and the given circle draw the tangent 
BC. 




Fig. 16. 



Plane Geometry 



Problem 19 



Through a Point on a Line, Bisecting the Angle Between Two Lines, Draw 
a Circle Which Shall he Tangent to the Given Lines. (Fig. 17.) 




Fig. 17. 



Let A be the point on a line bisect- 
ing the angle between BC and DE. 
Through A draw CE perpendicular to 
AF. Bisect the angles at C and E. 
The intersection G of the bisecting 
lines will be on ^F and at the center 
of the required circle. 



Problem 20 

Describe an Arc, Tangent to Two Given Arcs and at a Given Point 
on one of the Arcs. (Fig. 18.) 



Let A and B be the centers of the given arcs 
and C the point of tangency on the arc, whose 
center is B. Join A and B and draw BC through 
the given point. Make CE equal to the radius 
AD. 

Bisect AE, draw a perpendicular at its middle 
point and prolong to intersection with BC at F, 
which is the center of the arc required. 




Fig. 18. 



Problem 21 

To Construct a Pentagon having a Given Side AB. (Fig. 19.) 

At B erect a perpendicular BC, equal to one-half AB. Draw AC and 
make CD equal BC. Then BD is the radius of the 
circle circumscribing a pentagon having sides equal 
to AB. 

The radius of a given circle is the side of an in- 
scribed hexagon. 

The radius of a circle circumscribing a hexagon, 
is equal to the distance from the center of the hexa- 
gon to the extremity of one of its sides. 




Fig. 19. 



Plane Geometry 



21 




Problem 22 

To Construct an Ellipse when the Transverse and Conjugate Axes 
are Given. (Fig. 20.) 

Draw the axes AB and CD intersecting at G. From C, with one- 
half ^5 as a radius, cut AB dit E and F. Divide GB into any number 
of parts as at i, 2, 3, 4, 5. 

With £ as a center and ^ i as a 
radius, and with i^ as a center and 
radius B i, strike arcs cutting each 
other at i, i, above and below the 
transverse axis. 

Again with E and F as centers 
and A 2 and B 2, respectively as 
radii, describe arcs cutting each 
other at 2, 2. Find as many points as desired in the same way in both 
halves of the ellipse, then trace the curve. 

This construction depends on the property of an ellipse; that the sum 
of the distances from the foci to any point on the ellipse is equal to the 
transverse axis. 

Problem 23 

To Describe an Ellipse Mechanically when the Transverse and Con- 
jugate Axes are Known. (Fig. 21.) 

Draw the axes and determine the foci as in Problem 22. Drive two 
pins at the foci E and F. Fasten to each of the pins one end of a cord 

whose length is equal to that of the 
transverse axis. 

Then with a pencil, so placed 
within the loop of the cord as 
always to keep it taut and uniformly 
strained, trace one-half of the curve, 
from one extremity of the trans- 
verse axis to the other. The other 
half of the curve is traced by chang- 
ing the cord and pencil to the oppo- 
site side of the transverse axis. This 
method is seldom satisfactory on 
account of the unequal stretching 
of the cord. 

A better mechanical method of describing an ellipse is to place a 
straight edge along and above the transverse axis and another along and 




1° 


1 


A 


B C 




Fig. 21. 



22 



Plane Geometry 



at one side of the conjugate axis, as at AB and CD (Fig. 21), leaving a 
slight opening between the end of the straight edge CD and the transverse 
axis. 

There must also be a thin strip of wood with a hole for pencil point at 
A and small pins at B and C; AB being equal to one-half of the conju- 
gate axis; and AC equal to one-half the transverse axis. By moving 
this strip so that the pin B is always in contact with AB and the pin C 
in like contact with CD the upper half of the ellipse may be de- 
scribed. 

The straight edges are placed in corresponding positions on the 
opposite side of the transverse axis to describe the other half of the 
ellipse. 

Except where extreme accuracy is required, it is more convenient to 
approximate the ellipse with circular arcs. 
Thus: Lay o& AB and CD (Fig. 22) 
equal to the transverse and conjugate axes 
respectively. Make Oa and Oc equal to 
the difference between the serai-transverse 
and semi-conjugate axes, and ad equal to 
one-half ac. Set off Oe equal to Od. Draw 
di parallel to ac; join e and i and draw. the 
parallel lines dm and em. From m, with a 
radius mC, strike an arc cutting md and me. From i, with iD as a 
radius, strike an arc cutting id and ie. Then from d and e, with radius 
Ad, strike arcs closing the figure. 




The Parabola 

A parabola is a curve every point of which is equidistant from a line 
called the directrix and from a point on its axis called the focus. The 
directrix is a line perpendicular to the axis and at the same distance as 
the focus from the apex of the curve. 

A line perpendicular to the axis, drawn through the focus to the curve, 
is called the parameter. 

If a line be drawn from any point of the curve, perpendicular to the 
axis, the distance from the apex to the intersection of the perpendicular 
with the axis is called the abscissa of that point and the distance from 
the intersection at the axis to the curve is called the ordinate of that 
point. 

Abscissae of a parabola are as the squares of corresponding ordl- 
nates. 



The HypeTholsL 



23 



Problem 24 

To Construct a Parabola when the Focus and Directrix 
are Given. (Fig. 23.) 
Let AB he the directrix, and C the 
focus of a parabola. Bisect CD at E, which 
point is the apex of the curve. 

Then with C as a center and any radii, 
as C I, C 2, etc., strike arcs at i, 2 and 3, 
etc. From Z> as a center and with the 
radii equal to C i, C 2, C 3, etc., cut the 
axis at i', 2', 3', etc. Through these points 
draw lines parallel to AB. 

The intersection of corresponding parallels and arcs are points on the 
required curve. 

Problem 25 

To Construct a Parabola when an Abscissa and Its Corre- 
sponding Ordinate are Given. (Fig. 24.) 




Fig. 23. 



A 


^ 


A 


\\ 


/ 


TA. 


/■ 


\ A 


/ . 


\\ 


'^' F 


.^-^E Ad 



Fig. 24. 



Let BA be the given abscissa and AD 
the ordinate. 

Bisect AD at E. Draw EB, and EF 
perpendicular to EB. Set off BG and BK, 
each equal to AF. Then will G be the 
focus and LM (through K) perpendicular 
to AB, the directrix. Construct the curve 
as in Problem 24. 



The Hyperbola 

An hyperbola is a curve, such that the difference of the distances from 
any point of it to two fixed points is always equal to a given distance. 

The two fixed points are called the foci and the given distance is the 
transverse axis. The conjugate axis is a line perpendicular to the trans- 
verse axis at its middle point; and its length is equal to the side of a 
rectangle, of which the transverse axis is the other side and the distance 
between the foci, the diagonal. 



Problem 26 

To Construct an Hyperbola when the Foci and Transverse Axis are Given 

Let A and B be the foci and EF the transverse axis. From A set off 

AG equal to EF. Then, from ^ as a center and with any distance 

greater than AF z.°, 3. radius, strike an arc CD, cutting the transverse 



24 



Plane Geometry 




axis (prolonged) at H. From 5 as a center and HG as a radius, describe 
arcs cutting the arc CD at C and D. C and D will be points on the curve; 
in like manner any number of points are determined, through which the 
curve may be traced. 

Proceeding in the- same way on the opposite side 
of the conjugate axis, the other branch of the curve 
is constructed. 

The diagonals of a rectangle constructed on the 
transverse and conjugate axes are called the 
asymptotes and are lines to which the curve is 
tangent at an infinite distance. When the asymp- 
totes are at right angles the curve is called an equi- 
^'^- ^5- lateral hyperbola. 

It is a property of the equilateral hyperbola, that if the asymptotes 
be taken as the co-ordinate axes the product of the abscissa and ordinate 
of any point of the curve is equal to the corresponding product of the 
co-ordinates at any other point; or that the diagonal of a rectangle con- 
structed by the ordinate and abscissa of any point of the curve passes 
through the intersection of the axes. 

Problem 27 

Given the Asymptotes and any Point on the Curve, to Construct 
the Curve. (Fig. 26.) 



Let AB and ^G be the asymptotes and D the given 
point. Multiply AB by AE and divide the product 

AB XAE 



by any other distance AF; then AG 



AF 



and the intersection at / of lines through F and G, 
parallel to the axes, is another point on the curve. 





/ 


/ 


I 


/ 


\ 


\ 


n 


^ 


\ 




\\ 




^-^ 


^ 


^s 


^ 



F 

Fig. 



26. 



Properties of Plane Figures 

(i) In a right angle triangle, the square of the hypothenuse is equal 
to the sum of the squares of the other two sides. 

(2) In an equilateral triangle all the angles are equal. 

(3) In an isosceles triangle a line drawn from the vertex perpendicular 
to the base bisects the base and also the angle at the vertex. 

(4) An exterior angle of a triangle equals the sum of the two opposite 
angles. 

(5) Similar triangles have equal angles and the sides opposite to 
corresponding angles are proportional. 



Properties of Plane Figures 25 

(6) In any polygon, the sum of all the interior angles is equal to twice 
as many right angles as the figure has sides, less four right angles. 

(7) In any polygon the sum of all the exterior angles is equal to four 
right angles, or 360°. 

(8) The diagonals of any regular polygon intersect at the center 
of the figure. 

(9) A circle may be passed through any three points, not on the same 
straight line. 

(10) In the same circle, arcs are proportional to the angles at the 
center. 

(11) Any two arcs having the same angle at the center are propor- 
tional to their radii. 

(12) Areas of circles are proportional to the squares of their diameters 
or the squares of the radii, 

(13) A radius perpendicular to the chord of an arc bisects the arc 
and its chord. 

(14) A straight line tangent to a circle is perpendicular to the radius 
at the point of tangency. 

(15) An angle at the center of the circle is equal to twice the angle 
afthe circumference subtended by the same arc. 

(16) Angles at the circumference of a circle, standing on the same 
arc, are equal. 

(17) Any triangle inscribed in a semicircle is a right angled tri- 
angle. 

(18) In any triangle inscribed in a segment of a circle, the angles at 
the circumference are equal. 

(19) Parallel chords or a chord and a parallel tangent intercept 
equal arcs. 

(20) If two chords of a circle intersect, the rectangles made by the 
segments of the respective chords are equal. 

(21) If one of the chords is a diameter of the circle and the other is 
perpendicular to it, then one-half of the chord is a mean proportional 
between the segments of the diameter. 

(22) In any circle, with the center as the origin of co-ordinates, the 
sum of the squares of the abscissa and ordinate of any point is equal to 
the square of the radius, or x^ -\- y^ =^ R^. 

(23) In any ellipse with same origin, the square of the abscissa of any 
point multiplied by the square of the semi-conjugate axis plus the square 
of the ordinate of same point multiplied by the square of the semi- 
transverse axis is equal to the square of the product of the semi-axes. 

Thus: -BV _j_ j^2y2 = ^2^2^ where A and B are the semi-transverse 
and semi-conjugate axes. 



26 



Mensuration 



(24) In an ellipse, lines drawn from any point to the foci make equal 
angles with a tangent at that point. 

(25) The sum of the distances from any point of an ellipse to the foci 
is equal to the transverse axis. 

(26) If from any point of a parabola a line be drawn to the focus, and 
one parallel to the axis, they will make equal angles with the tangent at 
that point. 

(27) The apex of a parabola bisects the distance on the axis from the 
focus to the directrix. 

(28) The angle between two tangents to a parabola is equal to half 
the angle at the focus, subtended by the chord joining the points of 
tangency. 

(29) The area included between any chord of a parabola and the curve 
is equal to two-thirds that of the triangle formed by the chord and 
tangents through its extremities. 

(30) The difference between the focal distances of any point of an 
hyperbola is equal to the transverse axis. 

(31) The product of the perpendiculars from the foci to any tangent 
of an hyperbola is constant. 

(32) A tangent at any point of an hyperbola makes equal angles with 
the focal distances of the point. 



SECTION IV 
MENSURATION 



PLANE SURFACES 
Triangles 




The area of any triangle is equal to half the 
base multiplied by the altitude. (Fig. 27.) 
AB 



Area = 



XCD. 



To solve a triangle, three sides, two angles 
and one side or two sides and one angle must 
be given. 

The area of a parallelogram is equal to the 
base multiplied by the perpendicular distance 
between the sides =- AB X CD. (Fig. 28.) 



Fio. 2$. 




Triangles 



The area of a trapezoid is equal to half the 
sum of the parallel sides multiplied by the per- 
pendicular distance between them. (Fig. 29.) 



27 



A \. 



Area 



AB + CD 



X CE. 



Fig. 29. 




Fig. 30. 



The area of a trapezium is equal to the 
diagonal multiplied by half the sum of the 
perpendiculars dropped to it from the vertices 
of the opposite angles. (Fig. 30.) 



The area of any quadrilateral is found 
by multiplying the diagonal by one-half the 
sum of the perpendiculars dropped from the 
vertices of the opposite angles. (Fig. 31.) 
DE + BF 




Area = AC X 



Fig. 31. 




F E 
Fig. 32. 



If the diagonal falls without the figure, the 
area is equal to the product of the diagonal 
by half the difference of the perpendiculars. 
(Fig. 32.) 

Area =ABCD = AC X ^^~^^ . 



A polygon is a plane figure bounded by three or more straight lines; 
it is regular or irregular according as the lines bounding it are equal or 
unequal. 

If straight lines be drawn from the center of a regular polygon to each 
of the vertices of the interior angles, the polygon will be divided into as 
many isosceles triangles as it has sides. Each triangle will have for its 
base one of the sides of the polygon and for its altitude the perpendicular 
distance from the center of the polygon to that side. The area of the 
polygon is equal to the sum of the areas of all the triangles, and is 
found by multiplying one-half the sum of all the 
sides of the polygon by the perpendicular distance 
from the center to one of its sides. 

To find the area of an irregular polygon, divide 

the polygon into triangles and take the sum of 

their areas. 

Fig. 33. 

To Find the Area of Any Irregular Plane Figure 
Let C D EF G he any irregular figure. Draw any straight line AB 
as a base; through the ^extremities of the figure drop perpendiculars 




£3^56789 10 



28 Mensuration 

CA and FB to the base. Divide AB into any number of equal parts, 
say lo. Through the middle points of each of the equal divisions draw 
perpendiculars cutting the boundaries of the figure on opposite sides. 
Take the sum of the lengths of all these lines within the figure and divide 
such sum by the number of divisions; the' quotient is the mean width of 
the figure which multipHed by its length AB gives the area. 

TJ 

Thus: ab -{- cd + ef etc. = H; then — X AB equals the area of 
CDEFG. 

The Circle 

The ratio of the circumference of a circle to its diameter is equal to 
3.14159. This is represented by the Greek letter x, pronounced Pi. 

Let C = the circumference of any circle. 
D = the diameter of any circle. 
r = the radius of any circle. 
A = area of any circle. 

The areas of circles are as the squares of their diameters, or as the 
squares of their radii. 

C = 7rZ> = 3-14159 X D. 
C = 2-n-r = 6.28318 X r. 
A = irr"^ = 3.14159 X r^. 
^ = i,rZ>2 = 0.7854 X D\ 

A = — = 0.07958 X (?. 
47r 

A = 0.7854 X 4 r^' 

24' 

C 
D = - = 0.3183 X C. 



D = 2 Y - = 1.1284 Va. 



r = — = 0.5642 y/A, 

2ir 



The Ellipse 



59 



The Ellipse 

The ellipse is a curve formed by the intersection of a plane inclined 
to the axis of a cone or cyHnder, where the plane does not cut the base. 



(^ 






G 


V ' ■■ 





V 




-> 


^ 




Fig 


■ 34. 





To Find the Length of any Ordinate, HK or LM, Knowing the Two 
Diameters AB and CD, and the Abscisses OK and OM 



HK 



LM 



AB^ : CD^ :: AK X KB : HK^, 

./ CD^ X (AK X KB) 
V ' AB^ 

./AB^ {CM X MD) _ 



CD^ 



= ^ 
AB 

AB 
CD 



VAKxKBy 



VCM X MD. 



The circumference of an ellipse is found from the formula below, 
wherein D = transverse diameter and d = conjugate diameter. C = 

circumference = $.1415 d + 2 {D — d) '^ 



V{D + d) X {D + 2d) 

^ »/Z)2 + # (D - dY 
C = 3.i4i5V-- g;g— 



These formulas apply where large D is not more than five times as 
long as d. 

The area of an ellipse is equal to that of an annular ring of which the 
sum and difference of the radii of the limiting circles are respectively 
equal to the semi-axes of the ellipse. 

Thus TT (r2 - r'^) =Tr{r + r')X{r- r') ; then if {r + r') equals the semi- 
transverse axis equals A, and (r — r') equals the semi-conjugate axis 
equals B, the area of the ellipse equals tt {AB) or tt into the product of 
the semi-axes or into the product of the axes, divided by four. 



30 Mensuration 

SOLIDS 
The Prism 

A prism is a solid whose bases or ends are similar, equal and parallel 
polygons and whose sides are parallelograms. The prism is right or 
oblique according as the sides are perpendicular to or inclined to the ends; 
regular or irregular, as the ends are regular or irregular polygons. 

The surface of any prism is the sum of the areas of the sides added to 
that of the ends. 

To find the surface of a right prism, multiply the perimeter of its base 
by its altitude; to this product add the areas of the ends. 

The volume of any prism is equal to the area of its base multiplied 
by its altitude, or perpendicular distance between the ends. 

The volume of any frustum of a prism is equal to the product of the 
sum of all the edges (divided by their number), and the area of the cross 
section perpendicular to those edges. 

The Pyramid 

A p5n'amid is a solid having any polygon for its base; and for its sides 
triangles, terminating at one point called the apex 

The axis of a pyramid is a straight line from the apex to the center of 
gravity of its base. 

A pyramid is right or oblique according as the axis is perpendicular 
or inclined to the base; regular or irregular, as the base is a regular or 
irregular figure. 

The slant height is the distance from the vertex of any of the tri- 
angular sides to the middle point of its base. 

The surface of any pyramid is equal to the sum of the areas of all the 
triangles of which it is composed plus the area of the base. 

The surface of a right regular pyramid is equal to the perimeter of its 
base multiplied by half the slant height plus the area of the base. 

The volimie of any pyramid is equal to the area of the base multiplied 
by one-third of the altitude; or the perpendicular distance from the apex 
to the base. It is also equal to one-third the volume of a cylinder having 
the same base and altitude; or to one-half the volume of a hemisphere 
having the same base and altitude. 

The volumes of a pyramid, hemisphere and cylinder, having the same 
base and altitude are to each other as i, 2 and 3. 

Frustrum of a Pyramid 

The frustrum of a pyramid is the section between two planes which 
may or may not be parallel. 



folyhedra 31 

The slant height of any side of a frustrum of a p)nramid is measured 
from the middle points of the top and bottom sides of the trapezium 
• forming that side. 

To find the surface of any frustrum of apyramid, take the sum of the 
areas of all the trapeziums forming the sides, to which add the sum of 
the top and base. 

The surface of a frustrum of a right regular pyramid, where the top 
and base are parallel planes, is equal to one-half the sum of the perimeters 
of top and base multiphed by the slant height plus the sum of the areas 
of the top and base. 

The volume of any frustrvmi of any pyramid, with top and base 
parallel, is equal to one-third the perpendicular distance between top 
and base multiplied by the sums of the areas of top and base, and the 
square root of the product of those areas. 

Thus H, being the perpendicular and A and A' the areas of top and 
base, respectively, then the volume equals \ H X {A -{- A' -{- Va X A') 
or A" being equal to the area of a section midway between and parallel 
to base and top, the volume = V = I H {A +A' + 4A"). 

A prismoid is a solid having six sides, two of which are parallel but 
unequal quadrangles, and the other sides trapeziums. 

To find the Volume of a Prismoid 

Let A = area of one of the parallel sides. 
a = area of the other parallel side. 
M = area of cross section midway between and parallel to 

the parallel sides. 
L = perpendicular distance between the two parallel sides. 

Then . Volmne = LX (^A+^+AK"^ . 

The Wedge 

The wedge is a frustrum of a triangular prism. Its volimie is equal 
to the area of a right section multiplied by one-third the sum of the 
lengths of the three parallel edges. 

Let A equal area of section perpendicular to the axis of the prism and 
BC, DE and FG, the lengths of the parallel edges respectively. 

Then Volume of wedge = A (BC + DE+FG) ^ 

3 
Polyhedra 

A polyhedron is a solid bounded by plane surfaces. 
A regular polyhedron is one whose bounding faces are all equal and 
regular polygons. 



32 Mensuration 

There are five regular polyhedra as follows: 



Name 


Bounded by 


Surface 
= sum of sur- 
faces of all the 
faces 
= square of 
the length of 
one edge by 


Volume 
= product of 
cube of length 
of one edge by 




4 Equilateral triangles. . . 

6 squares 

8 Equilateral triangles.. . 
• 12 Equilateral pentagons. 
20 Equilateral triangles. . 


I . 7320 
6.000 
3.4641 
20.6458 
8.6602 


.1178 


Cube or hexahedron 


1. 000 




7 6631 




2.1817 







The Cylinder 

A cylinder may be defined as a prism, of which a section perpendicular 
to its axis is a circle. It may be right or oblique. 

The base of a right cylinder is a circle, that of an oblique cylinder an 
ellipse. 

The surface of any cylinder is equal to the product of the circumference 
of a circle whose plane is perpendicular to the axis of the cylinder, by 
the length of the axis, plus the area of the ends. 

The volume of a cylinder is equal to the area of a circle perpendicular 
to the axis multiplied by its altitude. 



The Cone 

A cone is a pyramid having an infinite number of sides. 

Cones are right or oblique according as their axes are perpendicular 
or inchned to their bases. 

The surface of a right cone is equal to the product of the perimeter 
of the base by half the slant height, plus the area of the base. 

The surface of an oblique cone, cut from a right cone having a circular 

base, is equal to the area of the base, multiplied by the altitude and 

divided by the perpendicular distance from the axis at the point where 

it pierces the base, to the surface of the cone, plus the area of the base; 

AH 
or the curved surface of the cone equals -zz-- Wherein A is the area 

K 

of the base, H the altitude and R the perpendicular. 

The volume of any cone is equal to the area of the base multiplied by 
one-third of the altitude. 

The volume of a cone is equal to one-third that of a cylinder, or one- 
half that of an hemisphere having same base and altitude. 



The Sphere 33 

The surface of a right circular frustrum of a cone with top and base 
parallel is found by adding together the circumferences of top and base, 
multiplying this sum by one-half the slant height; to this product add 
the area of top and base to get the total surface. 

The volume of a frustrum of any cone, with top and base parallel, is 
equal to one-third of the altitude multiplied by the sum of the areas of 
top and base plus the square root of the product of those areas, or equals 
i the altitude 



X (area of top + area of base + V^area of top X area of base). 



The Sphere 

A sphere is a solid generated by revolving a semicircle about its 
diameter. 

The intersection of a sphere with any plane is a circle. 
A circle cut by the intersection of the surface of a sphere and a plane 
passing through its center is a great circle. 

The volume of a sphere is greater than that of any other solid having 
an equal surface. 

The surface of a sphere equals that of four great circles. 
Surface = /^.Trr"^. 
= ttDK 
" = curved surface of a circumscribing cyhnder. 
" = area of a circle having twice the diameter of the sphere. 

The surface of a sphere is equal to that of a circumscribing cube 
multiplied by 0.5236. 

Surfaces of spheres are to each other as the squares of their diameters. 

Volume of a Sphere 

Volume = f7ry3 = 4.1888^3 
" =i7r2)3 = 0.52362)3 
" =1 volume of circumscribing cylinder. 
" = 0.5236 volume of circumscribing cube. 

Volumes of spheres are to each other as the cubes of their diameters. 



Radius of a sphere = 0.62035 "V^ volume. 



Circumference of sphere = v^59.2i76 volume. 

= V3.1416 X area of surface. 
_ Area of surface 
Diameter 



34 Mensuration 

The area of the curved surface of a spherical segment is equal to the 
product of the circumference of a great circle by the height of the seg- 
ment = ttDH, where D is the diameter of the sphere and H the height 
of the spherical segment. 

The curved surface of a segment of a sphere is to the whole surface 
of the sphere as the height of the segment is to the diameter of the 
sphere. 

To Find the Volume of a Spherical Segment 

Let R = radius of base of segment. 

H = height. 

Then volume of segment = ^TrH{2,B? + H^). 

To find the curved surface of a spherical zone, multiply the circum- 
ference of the sphere by the height of the zone. 

To find the volume of a spherical zone, let A and^' be the radii of 
the ends of the zone and H be the height and V the volume. 

Then V -- 

Guldin's Theorems 

(i) If any plane curve be revolved about any external axis situated 
in its plane, the surface generated is equal to the product of the perimeter 
of the curve and the length of the path described by the center of gravity 
of that perimeter. 

(2) If any plane surface be revolved about any external axis situated 
in its plane, the volume generated is equal to the area of the revolving 
surface multiplied by the path described by its center of gravity. 



CHAPTER II 

WEIGHTS AND MEASURES 

In the United States and Great Britain measures of length and weight 
are, for the same denomination, essentially equal; but liquid and dry 
measures for same denomination differ widely. The standard measure 
of length for both countries is that of the simple seconds pendulum, 
at the sea level, in the latitude of Greenwich; in vacuum and at a tem- 
perature of 62° F. 

The length of such a pendulum is 39.1393 inches; 36 of these inches 
constitute the standard British Imperial yard. This is also the stand- 
ard in the United States. 

The Troy pound at the U, S, Mint of Philadelphia is the legal standard 
of weight in the United States. 

It contains 5760 grains and is exactly the same as the Imperial Troy 
pound of Great Britain. 

The avoirdupois pound (commercial) of the United States contains 
7000 grains, and agrees with the British avoirdupois pound within o.ooi 
of a grain. 

The metric system was legalized by the United States in 1866 but its 
use is not obligatory. 

The metre is the unit of the metric system of lengths and was supposed 

to be one ten millionth, , of that portion of a meridian between 

10,000,000 

either pole and the equator. 

The metric measures of surface and volume are the squares and cubes 
of the metre, and of its decimal fractions and multiples. 

The metric unit of weight is the gramme or grain, which is the weight 
of a cubic centimeter of pure water at a temperature of 40° F. 

The legal equivalent of the metre as established by Act of Congress 
is 39-37 inches = 3.28083 ft. = 1.093611 yards. 

The legal equivalent of the gramme is 15.432 grains. 

The systems of weights used for commercial purposes in the United 
States are as follows: 

35 



36 Weights and Measures 

Troy Weight 

For Gold, Silver, Platinum and Jewels, except Diamonds and Pearls 
24 grains = i pennyweight (dwt.).' 

20 pennyweights = i ounce = 480 grains. 
12 ounces = i pound = 5760 grains. 

Apothecaries Weight 

{For Prescriptions only.) 
20 grains = i scruple O) 

3 scruples = i drachm (3) = 60 grains. 

8 drachms = i ounce (S) = 480 " 
12 ounces. = i pound (lb) = 5760 " 

Avoirdupois Weight 

For all Materials except those above named 
16 drachms or 437.5 grains = i ounce (oz.). 
16 ounces = i pound (lb.) = 7000 grains. 

28 pounds = I quarter (qr.). 

4 quarters ' = i hundredweight (cwt.) = 

112 lbs. 
20 hundredweight = i long or gross ton = 2240 lb. 

2000 pounds = I short or net ton. 

2204.6 pounds = I metric ton. 

I stone =14 pounds. 

I quintal =100 pounds. 

The weight of the grain is the same for all systems of weights. 
A troy ounce = i .097 avoirdupois ounces. 

An avoirdupois ounce = .91146 troy or apoth. ounce. 
A troy pound = .82286 avoirdupois pound. 

An avoirdupois pound = i . 21528 troy or apoth. pounds. 
The standard avoirdupois pound is equal to the weight of 27.7015 cu. 
in. distilled water at 39.2° F., at sea level and at the latitude of Green- 
wich. 

Long Measure 

12 inches = i foot = .3047973 metre. 

3 feet = I yard = 36 in. = .9143919 metre. 

5I yards = i rod, pole, perch = i6| feet = 198 in. 
40 rods = I furlong = 220 yards = 660 ft. 

8 furlongs = i statute mile = 320 rods = 1760yds. = 5280 ft. 

3 miles = I league = 24 furlongs =960 rods = 5 280 yds. 



Square Measure 37 

Land Measure 

7.92 inches = i link; 100 links (66 ft.) = i chain = 4 rods. 

10 chains = i furlong; 8 furlongs (80 chains) = i mile. 

10 square chains = i acre. 

Measures occasionally used 

y^5 inch = I point; 6 points-y^a in. = i Hne. 
1000 mils = I inch; 3 in. = i palm; 4 in. = i hand; 9 in. = i span. 
2 yards = i fathom = 6 feet; 120 fathoms = i cable length. 
A geographical (nautical) mile or knot = 6087.15 ft. = 1855.345 

metres = 1. 15287 statute miles. 
I knot = I minute of longitude or latitude at the equator. 

1° latitude at the equator = 68 . 70 statute miles. 
1° " " latitude 20° =68.78 
1° " " " 40° =69.00 " 
'1° " " " 60° =69.23 " 
1° " " " 90° =69.41 " 

Square Measure 

144 square inches = i square foot. 
9 " feet =1 " yard. 
30^ " yards =1 " rod, perch or pole = 272J sq. ft. 
40 " rods = I rood = 1210 sq. yds. = 108,908 sq. ft. 
4 roods (10 sq. chains) = i acre = 160 sq. rods = 4840 sq. yds = 
43,560 sq. ft. 
640 acres = i sq. mile = i section. 
An acre = a square whose side is 208.71 ft. 
A half acre = a square whose side is 147.581 ft. 
A quarter acre = a square whose side is 104.355 ft. 
A circular inch is the area of a circle i inch in diameter and = .7854 
sq. inches. 

I square inch = 1.2732 circular inches. 

A circular mil is the area of a circle i mil or .001 in. in diameter. 

looo^ mils or 1,000,000 circular mils = i circular inch. 

I square inch = 1,273,239 circular mils. 

A cylinder, i inch in diameter and i foot high, contains: 
1 . 3056 U. S. gills. 
.2805 U. S. dry pints. 
.3246 U. S. liquid pints. 
A cylinder, one foot in diameter and i foot high, contains: 
1357-1712 cubic inches. i'8S.oo64 U. S. liquid gills. 

.7854 " feet. ^ 47.0016 U.S. " pints. 

.02909 " yards. 23.5008 U.S. " quarts. 



38 



Weights and Measures 



5.8752 U. S. liquid gallons. 
40.3916 U. S. dry pints. 
20.1958 U. S. " quarts. 



2.5254 U. S. dry pecks. 
0.63112U.S. " bushels. 



Liquid Measure 

{United States only) 
4 gills = I pint = 28.875 cubic inches. 

2 pints = I quart= 57.75 cu. ins. = 8 gills. 

4 quarts = i gallon =231 cu. in. = 8 pts. = 32 gills. 
31I gallons = I barrel = 126 quarts = 4.211 cu. ft. 
63 gallons = I hogshead. 
- 2 hogsheads = i pipe or butt. 
2 pipes = I tun. 

A puncheon contains 84 gallons. 
A tierce contains 42 gallons. 

A cube 1. 615 ft. on edge contains 3.384 U. S. struck bushels; or 31I 
gallons = I bbl.; or 4.21 1 cu. ft. 



Approximate 
measure 


Diameter 


Height 


Approximate 
measure 


Diameter 


Height 


I Gill 
i Pint 
I Pint 
I Quart 


Inches 
1.7s 
2.25 
3-50 
3.50 


Inches 
3 
31 
3 
6 


1 Gallon 

2 Gallons 
8 Gallons 

10 Gallons 


Inches 

7 

7 
14 
14 


Inches 
6 
12 
12 
15 



The basis of this measure is the old British wine gallon of 231 cubic 
inches; or 8.3388 lbs. of distilled water at 39° F. and 30" barometer. 
A cubic foot contains 7.48 gallons. 

Apothecaries' or Wine Measure 



Measure 


Symbol 


Pints 


Fluid 
ounces 


Fluid 
drachms 


Minims 


Cubic 
inches 


Weight of water 


Ounces 
avoir. 


Grains ' 


I Minim 

I fluid drachm . 
I fluid ounce... 

I pint 


m 

% 


Cong. 


I 
8 


I 

16 
128 


I 
8 

128 
1024 


I 
60 
480 

7680 
61440 


0.0038 
0.2256 
1.8047 

28.875 
231 


I 043 
Pounds 
avoir. 
1.043 
8.345 


0-95 

57.05 

456.4 

7301.9 


I gallon 


S8415 



r 



British Imperial Liquid and Dry Measures 

Dry Measure 

{United States only) 



39 



2 pints = I quart = 67.2006 cubic inches = 1. 163 65 liquid quarts. 
4 quarts = i gallon = 8 pints = 268.80 cubic inches = 1. 16365 liq. gal. 
2 gallons = I peck = 16 pints = 8 qts. = 537.60 cu, inches. 
4 pecks = I struck bu. = 64 pints = 32 qts. = 8 gallons = 2150.42 cu. in. 
The old Winchester struck bushel containing 2150.42 cubic inches or 
77.627 pounds, avoirdupois, of distilled water at its maximum density- 
is the basis of this table. 

Its legal dimensions are those of a cylinder 18^ inches in diameter and 
8 inches deep. When heaped, the cone must not be less than 6 inches 
high; (the bushel) containing 1.5555 cubic feet and equal to i| struck 
bushels. 

Miscellaneous Measures 

12 pieces = i dozen. 20 pieces = i score. 

12 dozen = i gross. 24 sheets = i quire. 

12 gross = I great gross. 20 quires = i ream. 

2 pieces = i pair. 

Weights of Given Volumes of Distilled Water at 70° F, 

United States Liquid Measure 
I gill = . 26005 lbs. 
I pint = 1 . 1402 " 
I quart = 2.0804 " 
I gallon = 8 lbs. 5 J oz. = 8.345 lbs. 
I barrel = 31I gals. = 262.1310 lbs. 

United States Dry Measure 



I pint 

I quart 

I gallon 

I peck 

I bushel (struck) 



= 1. 2 104 lbs. 
= 2.4208 " 

= 9.6834 " 
= 19.3668 " 
= 77-4670 " 



British Imperial Liquid and Dry Measures 

Liquid and Dry Measures 
.31214 lbs. avoir, of distilled water. 
1.24858 



I gill = 

I pint = 

I quart = 

I gallon = 

I peck = 19.977^ 

I bushel = 79.9088 



2.49715 
9.9886 



40 



Weights and Measures 



This system supersedes the old ones throughout Great Britain, and, 
is based on the Imperial gallon of 277.274 cubic inches, equal to 10 pounds 
avoirdupois of pure water at 62° F., 30 in. Bar. 



I Utre 

I centilitre 

I decilitre 

I decalitre 

I metre or stere =2198.0786 



Metric Measures 

= 2. 1 98 1 lbs. avoir, of pure water. 

.02198 " " " " "= 153,866 gr. 
.2198 '* " " " " = 3.516902. 

i-».^ It tc IC t c 

= 21 .' 



Metric Measures of Length in U. S. Standard 





Inches 


Feet 


Yards 


Miles 


Millimetre* 


.039370 
.393704 
3-93704 
39-3704 
393-704 
Road 
measiires 


.003281 
.032809 
.328087 
3.28087 
32.80869 
328.0869 
3280.869 
32808.69 


.1093623 
1.093623 
10.93623 
109.3623 
1093.623 
10936.23 








Decimetre 

MetreJ 




Decametre 
Hectometre 
Kilometre 
Myriametre i 


.062137s 
.6213750 







About 5V of an inch. t About I of an inch. t About 3 feet 3§ inches. 



Metric Square Measure by U. S. Standard 



Measures 



Square millimetre 

Square centimetre — 
Square decimetre. . . . 
Square meter or cen- 

taf e 

Square decametre or 

• aire 

Square decare* 

Hectare 

Square kilometre 

Square myriametre . . 



Square inches Square feet Square yards Acres 



.001550 
.155003 
15.5003 



1550.03 
155003 



Square miles 
.3861090 
38.61090 



.00001076 
.00107641 
. 10764101 

10.764101 

1076. 4101 
10764. lOI 
107641.01 
10764101 



.0000012 
.0001196 
.0119601 

I . 19601 

119.6011 
1196.011 
11960.11 
1196011 



.000247 

.024711 
.247110 
2.47110 
247.110 
24711.0 



Seldom used. 



Metric Weights, Reduced to Avoirdupois 



41 



Metric, Cubic or Solid Measure by U. S. Standard 



Millilitre or cubic cen- 
timetre 

Centilitre . 

Decilitre , 

Litre or cubic decimetre 
Decalitre or centistere . . 



Hectolitre or decistere . 



Kilolitre or cubic metre 
or stere 



Myrialitre or decastere. 



Cubic inches 
.0610254 

.610254 
6.10254 

61.0254 
610.254 

Cubic feet 
.353156 

3-53156 

35.3156 

353.156 



Liquid 



Dry 
Liquid 



Dry 
Liquid 



Dry 
Liquid 



Dry 



Liquid 



Dry 
Liquid 



Dry 

Liquid 



Dry 
Liquid 



Dry 



.0084537 gill. 



.0018162 pint. 
.084537 gill. 



.018162 pint. 
.84537 gill. 



. 18162 pint. 

1. 05671 quart = 2.1134 pints. 



,11351 peck = .9031 qt. = 1.816 pts. 



2.64179 gallons 



.283783 bu. = I.1351 pks. = 9.081 qts. 
26.4179 gallons. 



2.83783 bushel. 
264.179 gallons 



28.3783 bushels 
2641.79 gallons 



5.78 bushels 



= 1.3080 cu. yd. 
= 13.080 cu. yd. 



Metric Weights, Reduced to Avoirdupois 



Measure 


Avoirdupois 


Milligramme 

Centigramme 

Decigramme 

Gramme. . . 


.015432 grains 
.15432 
1.5432 
15.432 " 






Decagramme 

Hectogramme 

Kilogramme 

Myriagramme 

Quintal ' .. ... 


.022046 lbs. 
.22046 " 
2.2046 " 
22.046 
220.46 " 


Tonneau, millier or tonne 


2204.6 " 



The base of the French system of weights is the gramme; which is 
the weight of a cubic centimeter of distilled water at maximum density, 
at the sea level and at the latitude of Paris, Barometer 29.922 inches. 



4^ 



Weights and Measures 



Metric Lineal Measure 





Metres 


Inches 


Feet 


Yards 


Miles 


Millimetre 


.001 
.01 

.1 

I 

10 

lOO 

lOOO 

lOOOO 


.03937 
-3937 
3-937 
39-3685 


.00328 
.0328 
.3280 
3.2807 
32.807 
328.07 
3280.7 
32807 






Centimetre 






Decimetre 

Metre 


. 10936 
1.0936 
10.936 
109.36 
1093-6 
10936 

























Metric Square Measure 



Measures 

V 


Square 
metres 


Square 
inches 


Square 
feet 


Square 
yards 


Acres 


Square centimetre.... 

decimetre 

" centare 

Are 


.01 
.1 
I 
10 
100 


.155 
15.5 
1,549-88 
154,988 


. 10763 
10.763 
1,076.3 
107,630 


.01196 
1.196 
119. 6 
11,959 


.00025 
.0247 














Acres 


Square miles 


Square kilometre 

" myriametre. . 






247 
24,708 


.3860' 
38.607 


I 



Metric, Cubic or Solid Measure 



Measures 


Cubic 
metres 


Cubic 
inches 


Cubic feet 


Cubic 
yards 


OiiHif rpntimp+rf 


.0001 

.001 

.01 

I 

10 
100 


.0610165 
61.0165 
610.165 
6101.6s 


.353105 
3.53105 
35.3105 
353. los 
3531.05 












Decimstere 


. 13078 


Stere 


1.3078 






13.078 






130.78 









Circular Measure 



43 



Metric Weights 



Weight 


Grammes 


Troy grains 


Avoirdupois 
ounces 


Avoirdupois 
pounds 




.001 
.01 
.1 
I 

10 

100 

1,000 

10,000 

100,000 

1,000,000 


.01543 
.1543 
1.543 
15.43316 


.03528 
.3528 
3.52758 
35.2758 












Gramme 

Decagramme 

Hectogram.me 


.0022047 
.022047 




.2204737 


Kilogramme 

Myriagramme 

Quintal 




2 . 204737 




22.04737 






220.4737 








2204.737 











Metric Dry and Liquid Measures 




Measures 


Litres 


Cubic inches 


Cubic feet 


Millilitre 

Centilitre 

Decilitre 


.001 
.01 
.1 
I 
10 
100 
i,ooo- 
10,000 


.061 

.61 

6.1 

61.02 

610.16 




Litre 








Hectolitre 


3-531 


Kilolitre 




35.31 


Myrialitre 




353.1 









Circular Measure 

60 seconds (") i minute ('). 

60 minutes (') i degree (°). 

90 degrees (°) i quadrant. 

360 degrees (°) circumference. 

Time 

60 seconds i minute. 

60 minutes i hour. 

24 hours I day. 

7 days I week. 

365 days, s hours, 48 minutes, 48 seconds = i year. 
Every year whose number is divisible by 4 is a leap year and contains 
366 days. 

The Centismal years are leap years only when the number of the year 
is divisible by 400. 



44 



Weights and Measures 



Board and Timber Measure 

The unit of measurement is a board 12 inches square by one inch thick. 

To ascertain the number of feet board measure in a plank or piece of 
square timber, multiply the length by the breadth in feet and by the 
thickness in inches. 

To find the cubic contents of a stick of timber (all the measurements 
being reduced to feet), take one-fourth the product of the mean girth by 
the diameter and the length. 

To find the cubic contents of square timber, reduce all measurements 
to feet, then the product of the length by the breadth and thickness will 
be the volume in cubic feet. 

Miscellaneous Measures and Weights 

I barrel of flour weighs 196 pounds. 

I barrel of salt weighs 280 " 

I barrel of beef or pork weighs 200 " 

I bushel of salt (Syracuse) weighs 56 " 

Anthracite coal (broken) averages 54 lbs. to the cubic foot. 

Bituminous coal (broken) averages 49 " " " " " 



Cement (Portland) 
Gypsum (ground) 
Lime (loose) 
Lime (well-shaken) 
Sand 



weighs 



96 lbs. 


to the bushel, 


70 " 


a a c< 


70 " 


a t. a 


80 " 


u i( a 


98 " 


" " cubic : 



or 1, 181 tons 
to the cu. yd. 



Useful Factors 



Inches X 

" X 

" X 

Square inches X 

" X 

Cubic inches x 

" X 

" X 

Feet X 

" X 

Square feet X 

" X 

Cubic feet X 

" X 

" X 



0.08333 = feet 

0.02778 = yards 

0.00001578 = miles 



0.00695 
0.0007716 

0.00058 

0.0000214 

0.004329 

o 3334 
0.00019 

144.0 
0.II12 

1728 

o 03704 
7.48 



= square feet 
= square yards 

= cubic feet 
= cubic yards 
= U. S. gallons 

= yards 
= miles 

= square inches 
= square yards 

= cubic inches 
= cubic yards 
= U. S. gallons 



Measures of Work, Power and Duty 45 

Useful Factors — {Continued) 

Yards X 36 = inches 

" ., X 3 =feet 

" X 0.0005681 = miles 

Square yards X i ,296 = square inches 

" " X 9 = square feet 

Cubic yards X 46,656 = cubic inches 

" X 27 = cubic feet 

Miles X 63,360 = inches 

" X 5,280 =feet 

" X 1 ,760 = yards 

Avoirdupois ounces X .0.0625 = pounds 

X 0.0000312s =tons 

" pounds X 16 = ounces 

" " X .001 = hundredweight 

" " X .oooS = tons 

*' " 27.681 = cubic inches of 

water at 39.2° F 

" tons X 32,000 = ounces 

" " X 2,000 = pounds 

Watts X 0.00134 = horse power 

Horse power X 746 = watts 

Weight of round iron per foot = square of diameter in quarter inches -f- 6. 

Weight of flat iron per foot = width X thickness X io-3- 

Weight of flat plates per square foot = 5 pounds for each 1-8 inch thickness. 

Measures of Work, Power and Duty 

Work is the result of expenditure of energy in overcoming resistance. 

The unit of work is the pressure of one pound exerted through a distance 

of one foot and is called one foot pound. 

Horse Power. — Term employed to measure the quantity of work. 

The unit is one horse power; or the quantity of work performed in 

raising 33,000 lbs., one foot in one minute 

= 33,000 foot pounds per minute 

= 550 foot pounds per second 

= 1,980,000 foot pounds per hour. 

A heat unit is the amount of heat required to raise one pound of water 

at maximum density 1° F., or i pound of water from 39"^ F. to 40** F. = 

778 foot pounds. 

One horse power = 2545 heat units per hour 

33,000 . , 

= z— = 42.146 heat units per mmute 

s= .7021 heat units per second. 



46 



Mathematical Tables 



Table of Squares, Cubes, Square Roots and Cube 
Roots of Numbers from .i to io 



No. 


Square 


Cube 


Square 
root 


Cube 
root 


No. 


Square 


Cube 


Square 
root 


Cube 
root 


.1 


.OI 


.001 


.3162 


.4642 


4.1 


16.81 


68.921 


2.025 


1. 601 


.15 


.0225 


.0034 


.3873 


.5313 


4.2 


17.64 


74.088 


2.049 


1. 613 


.2 


.04 


.008 


.4472 


.5848 


4.3 


18.49 


79.507 


2.074 


1.626 


.25 


.0625 


.0156 


.500 


.6300 


4.4 


19.36 


85.184 


2.098 


1.639 


.3 


.09 


.027 


■ 5477 


.6694 


4.5 


20.25 


91 . 125 


2. 121 


1. 651 


.35 


.1225 


.0429 


.5916 


.7047 


4.6 


21.16 


97.336 


2.145 


1.663 


.4 


.16 


.064 


.6525 


.7368 


4.7 


22.09 


103.823 


2.168 


1.675 


■ 45 


.2025 


.0911 


.6708 


.7663 


4.8 


23.04 


110.592 


2. 191 


1.687 


.5 


.25 


.125 


.7071 


.7937 


4-9 


24.01 


117.649 


2.214 


1.698 


• 55 


.3025 


.1664 


.7416 


.8193 


5 


25 


125 


2.2361 


1. 710 


.6 


.36 


.216 


.7746 


.8434 


5.1 


26.01 


132.651 


2.258 


1. 721 


.65 


• 4225 


.2746 


.8062 


.8662 


5.2 


27.04 


140.608 


2.280 


1.732 


.7 


.49 


.343 


.8367 


.8879 


5.3 


28.09 


148.877 


2.302 


1.744 


.75 


.562s 


.4219 


■.8660 


.9086 


5.4 


29.16 


157.464 


2.324 


1. 754 


.8 


.64 


.512 


.8944 


.9283 


5.5 


30.25 


166.375 


2.345 


1.765 


.85 


.7225 


.6141 


.9219 


.9473 


5.6 


31.36 


175.616 


2.366 


1.776 


•9 


.81 


.729 


.9487 


.9655 


5-7 


32.49 


.185.193 


2.387 


1.786 


.95 


.9025 


.8574 


.9747 


.9830 


5.8 


33.64 


195. 112 


2.408 


1.797 


I 


I 


I 


I 


I 


5.9 


34.81 


205.379 


2.429 


1.807 


I-05 


I . 1025 


1. 158 


1.025 


1. 016 


6 


36 


216 


2.4495 


1.8171 


I.I 


I. 21 


I 331 


1.049 


1.032 


6.1 


37.21 


226.981 


2.470 


1.827 


1.15 


1.3225 


1. 521 


1.072 


1.048 


6.2 


38.44 


238.328. 


2.490 


1.837 


1.2 


1.44 


1.728 


1.095 


1.063 


6.3 


39.69 


250.047 


2.510 


1.847 


1.25 


1.5625 


1.953 


1. 118 


1.077 


6.4 


40.96 


262.144 


2.530 


1.857 


1.3 


1.69 


2.197 


1. 140 


1. 091 


6.5 


42.25 


274.625 


2.550 


1.866 


1.35 


1.8225 


2.460 


1. 162 


1. 105 


6.6 


43.56 


287.496 


2.569 


1.876 


1.4 


1.96 


2.744 


1 . 183 


1. 119 


6.7 


44.89 


300.763 


2.588 


I -885 


1-45 


2.1025 


3.049 


1.204 


1. 132 


6.8 


46.24 


314.432 


2.608 


1.89s 


1.5 


2.25 


3.375 


1.2247 


I. 1447 


6.9 


47.61 


328.509 


2.627 


1.904 


1.55 


2.4025 


3.724 


1.245 


1. 157 


7 


49 


343 


2.6458 


I. 9129 


1.6 


2.56 


4.096 


1.265 


1. 170 


7.1 


50.41 


357.911 


2.665 


1.922 


1.65 


2.7225 


4.492 


1.285 


1. 182 


7.2 


51.84 


373.248 


2.683 


1. 931 


1.7 


2.98 


4.913 


1.304 


1. 193 


7.3 


53.29 


389.017 


2.702 


1.940 


1.75 


3 0625 


5.359 


1.323 


1.205 


7.4 


54.76 


405.224 


2.720 


1.949 


1.8 


3.24 


5.832 


1.342 


1. 216 


7.5 


56.25 


421.875 


2.739 


1.957 


1.85 


3 4225 


6.332 


1.360 


1.228 


7.6 


57.76 


438.976 


2.757 


1.966 


1-9 


3.61 


6.859 


1.378 


1.239 


7.7 


59.29 


456.533 


2.775 


1. 975 


1.95 


3.802s 


7.415 


1.396 


1.249 


7.8 


60.84 


474.552 


2.793 


1.983 


2 


4 


8 


I. 4142 


1.2599 


7.9 


62.41 


493.039 


2. 811 


1.992 


2.1 


4.41 


9.26 


1.449 


1. 281 


8 


64 


512 


2.8284 


2 


2.2 


4.84 


10.648 


1.483 


1. 301 


8.1 


65.61 


531.441 


2.846 


2.008 


a. 3 


5.29 


12.167 


1. 517 


1.320 


8.2 


67.24 


551.368 


2.864 


2.017 


2-4 


5. 76 


13.824 


1.549 


1.339 


8.3 


68.89 


571.787 


2.881 


2.025 


2.5 


6.25 


15.625 


1. 581 


1.357 


8.4 


70.56 


592.704 


2.898 


2.033 


2.6 


6.76 


17.576 


1. 612 


1.375 


8.5 


72.25 


614.125 


2.915 


2.041 


2.7 


7.29 


19.683 


1.643 


1.392 


8.6 


73.96 


636.056 


2.933 


2.049 


2.8 


7.84 


21.952 


1-673 


1.409 


8.7 


75.69 


658.503 


2.950 


2. 057 


2.9 


8.41 


24.389 


1.703 


1.426 


8.8 


77.44 


681.472 


2.966 


2.065 


3 


9 


27 


I. 7321 


1.442 


8.9 


79.21 


704.969 


2.983 


2.072 


3.1 


9.61 


29.791 


1. 761 


1.458 


9 


81 


729 


3 


•2.081 


3.2 


10.24 


32.768 


1.789 


1.474 


9.1 


82.81 


753.571 


3.017 


2.088 


33 


10.89 


35.937 


1. 817 


1.489 


9.2 


84.64 


778.688 


3.033 


2.095 


3.4 


11.56 


39.304 


1.844 


1.504 


9.3 


86.49 


804.357 


3.050 


2.103 


35 


12.25 


42.875 


1. 871 


1. 518 


9.4 


88.36 


830.584 


3.066 


2. no 


3.6 


12.96 


46.656 


1.897 


1.533 


9.5 


90.25 


857.375 


3.082 


2. 118 


37 


13.69 


50.653 


1.924 


1.47 


9.6 


92.16 


884.736 


3.098 


2.125 


3.8 


14.44 


54.872 


1.949 


1.560 


9.7 


94.09 


912.673 


3. 114 


2.133 


3-9 


15.21 


59.319 


1.975 


1.574 


9.8 


96.04 


941 . 192 


3.130 


2.140 


4 


16 


64 


2 


1.5874 


9.9 


98.01 


970.299 


3.146 


2.147 



V 



Table of Squares, Cubes, Square Roots and Cube Roots 47 



Table of Squares, Cubes, Square Roots and Cube Roots 
OF Numbers from i to idoo 

Remark on the Following Table. Wherever the effect of a fifth decimal in the 
roots would be to add i to the fourth and final decimal in the table, the addition has 
been made. 



No. 


Square 


Cube 


Square 
root 


Cube 
root 


No. 
50 


Square 


Cube 


Square 
root 


Cube 
root 


I 


I 


I' 






2,500 


125,000 


7.0711 


3.6840 


2 


4 


8 


I. 4142 


1.2599 


51 


2,601 


132,651 




1414 


3.7084 


3 


9 


27 


I. 7321 


1.4422 


52 


2.704 


140,608 




2111 


3.7325 


4 


16 


64 


2 


1.5874 


53 


2,809 


148,877 




2801 


3.7563 


s 


25 


125 


2.2361 


I . 7100 


♦ 54 


2.916 


157.464 




3485 


3.7798 


6 


36 


216 


2.4495 


1.8171 


55 


3.02s 


166,375 




4162 


3.8030 


7 


49 


343 


2.6458 


I. 9129 


56 


3.136 


175,616 




4833 


3.8259 


8 


64 


512 


2.8284 


2 


57 


3.249 


185.193 




5498 


3.8485 


9 


81 


729 


3 


2.0801 


58 


3.364 


195,112 




6158 


3.8709 


10 


100 


1,000 


3.1623 


2.1544 


59 


3,481 


205.379 




6811 


3.8930 


II 


121 


1,331 


3.3166 


2.2240 


60 


3.600 


216,000 




7460 


3.9149 


12 


144 


1,728 


3.4641 


2.2894 


61 


3.721 


226,981 




8102 


3.9365 


13 


169 


2,197 


3.6056 


2.3513 


62 


3.844 


238,328 




8740 


3-9579 


14 


196 


2,744 


3.7417 


2.4101 


63 


3,969 


250,047 




9373 


3.9791 


IS 


225 


3,375 


3.8730 


2.4662 


64 


4.096 


262,144 


8 




4 


16 


256 


4,096 


4 


2.5198 


65 


4.225 


274,625 


8 


0623 


4.0207 


17 


289 


4,913 


4.1231 


2.5713 


66 


4,356 


287,496 


8 


1240 


4.0412 


18 


324 


5.832 


4.2426 


2.6207 


67 


4,489 


300,763 


8 


1854 


4 -0615 


19 


361 


6,859 


4.3589 


2.6684 


68 


4.624 


314,432 


8 


2462 


4.0817 


20 


400 


8,000 


4.4721 


2.7144 


69 


4,761 


328,509 


8 


3066 


4.1016 


21 


441 


9,261 


4.5826 


2.7589 


70 


4,900 


343.000 


8 


3666 


4.1213 


22 


484 


10,648 


4.6904 


2.8020 


71 


5,041 


357,911 


8 


4261 


4-1408 


23 


529 


12,167 


4.7958 


2.8439 


72 


5,184 


373.248 


8 


4853 


4.1602 


24 


576 


13,824 


4.8990 


2.8845 


73 


5,329 


389,017 


8 


5440 


4.1793 


25 


625 


15,625 


5 


2.9240 


74 


5,476 


405,224 


8 


6023 


4.1983 


26 


676 


17.576 


5.0990 


2.9625 


75 


5,625 


421,875 


8 


6603 


4.2172 


27 


729 


19,683 


5.1962 


3 


76 


5,776 


438,976 


8 


7178 


4.2358 


28 


784 


21,952 


5.2915 


3-0366 


77 


5,929 


456,533 


8 


7750 


4.2543 


29 


841 


24,389 


5.3852 


3.0723 


78 


6,084 


474,552 


8 


8818 


4.2727 


30 


900 


27,000 


5.4772 


3.1072 


79 


6,241 


493.039 


8 


8882 


4.2908 


31 


961 


29,791 


5.5678 


3.1414 


80 


6,400 


512,000 


8 


9443 


4.3089 


32 


1,024 


32,768 


5.6569 


3.1748 


81 


6,561 


531,441 


9 




4.3267 


33 


1,089 


35.937 


5.7446 


3.2075 


82 


6,724 


551,368 


9 


05S4 


4.3445 


34 


1,156 


39,304 


5.8310 


3.2396 


83 


6,889 


571,787 


9 


1 104 


4.3621 


35 


1.225 


42.875 


5.9161 


3.2711 


84 


7,056 


592,704 


9 


1652 


4.3795 


36 


1,296 


46.656 


6 


3.3019 


85 


7.225 


614,125 


9 


2195 


4.3968 


37 


1,369 


50.653 


6.0828 


3.3322 


86 


7,396 


636,056 


9 


2736 


4.4140 


38 


1,444 


54.872 


6.1644 


3.3620 


87 


7.S69 


658,503 


9 


3274 


4.4310 


39 


1. 521 


59.319 


6.2450 


3.3912 


88 


7,744 


681,472 


9 


3808 


4.4480 


40 


1,600 


64,000 


6.3246 


3.4200 


89 


7,921 


704,969 


9 


4340 


4.4647 


41 


1,681 


68,921 


6.4031 


3.4482 


90 


8,100 


729,000 


9 


4868 


4.4814 


42 


1,764 


74.088 


6.4807 


3.4760 


91 


8,281 


753,571 


9 


5394 


4.4979 


43 


1,849 


79.507 


6.5574 


3 -5034 


92 


8,464 


778,688 


9 


5917 


4.S144 


44 


1,936 


85.184 


6.6332 


3.5303 


93 


8,649 


804,357 


9 


6437 


4.5307 


45 


2,025 


91.125 


6.7082 


3.5569 


94 


8,836 


830,584 


9 


6954 


4.5468 


46 


2,116 


97.336 


6.7823 


3.5830 


95 


9,025 


857,375 


9 


7468 


4.5629 


47 


2,209 


103,823 


6.8557 


3.6088 


96 


9>2i6 


884,736 


9 


7980 


4.5789 


48 


2,304 


110,592 


6. 9282 \ 


3.6342 


97 


9,409 


912,673 


9 


8489 


4.5947 


49 


2,401 


117,649 


7 


3-6593 


98 


9,604 


941,192 


9 


8995 


4.6104 



48 



Mathematical Tables 



Table of Squares, Cubes, Square Roots and Cube Roots 
OF Numbers from i to iooo — (Continued) 



No. 


Square 


Cube 


Square 
root 


Cube 
root 


No. 
152 


Square 


Cube 


Square 
root 


Cube 
root 


99 


9.801 


970,299 


9-9499 


4.6261 


23,104 


3.511.808 


12.3288 


5.3368 


ICXD 


10,000 


1,000.000 


10 


4.6416 


153 


23.409 


3,581.577 


12.3693 


5.3485 


lOI 


10,201 


1.030,301 


10.0499 


4.6570 


154 


23,716 


3,652,264 


12.4097 


5.3601 


I02 


10,404 


1,061,208 


10.0995 


4.6723 


155 


24.025 


3,723,875 


12.4499 


5.3717 


103 


10,609 


1,092,727 


10.1489 


4-6875 


156 


24.336 


3,796,416 


12.4900 


5.3832 


104 


10,816 


1,124.864 


10.1980 


4.7027 


157 


24,649 


3,869,893 


12.5300 


5.3947 


105 


11,025 


1.157,625 


10.2470 


4-7177 


158 


24.964 


3,944.312 


12.5698 


5.4061 


106 


11,236 


1,191,016 


10 . 2956 


4.7326 


159 


25,281 


4,019,679 


12.6095 


5.417s 


107 


11,449 


1,225,043 


10.3441 


4-7475 


160 


25,600 


4.096,000 


12.6491 


5.4288 


108 


11,664 


1.259.712 


10.3923 


4 . 7622 


161 


25.921 


4,173.281 


12.6886 


5.4401 


109 


11,881 


1.295.029 


10.4403 


4.7769 


162 


26,244 


4,251,528 


12.7279 


5.4514 


no 


12,100 


1,331,000 


10 . 4881 


4.7914 


163 


26,569 


4.330,747 


12.7671 


5.4626 


III 


12,321 


1.367,631 


10.5357 


4.8059 


164 


26,896 


4.410,944 


12.8062 


5.4737 


112 


12,544 


1,404,928 


10.5830 


4-8203 


165 


27.225 


4,492.125 


12.8452 


5.4848 


113 


12,769 


1.442,897 


10.6301 


4-8346 


166 


27,556 


4,574.296 


12.8841 


5.4959 


114 


12,996 


1. 481. 544 


10.6771 


4.8488 


167 


27,889 


4.657.463 


12.9228 


5.5069 


115 


13,225 


1.520,875 


10.7238 


4.8629 


168 


28,224 


4.741.632 


12.9615 


5.5178 


116 


13,456 


1.560,896 


10.7703 


4.8770 


169 


28,561 


4.826,809 


13 


5.5288 


117 


13,689 


1,601,613 


10.8167 


4.8910 


170 


28,900 


4,913,000 


13.0384 


5.5397 


118 


13,924 


1.643.032 


10.8628 


4.9049 


171 


29.241 


5.000,211 


13.0767 


5.5505 


119 


14,161 


1.685,159 


10.9087 


4.9187 


172 


29,584 


5.088,448 


13.1149 


5.5613 


120 


14.400 


1,728,000 


10.9545 


4-9324 


173 


29,929 


5,177.717 


13.1529 


5.5721 


121 


14,641 


1,771,561 


II 


4-9461 


174 


30,276 


5,268,024 


13.1909 


5.5828 


122 


14.884 


1,815,848 


11.0454 


4-9597 


175 


30,625 


5.359,375 


13.2288 


5.5934 


123 


15.129 


1,860,867 


11.0905 


4-9732 


176 


30,976 


5,451,776 


13.2665 


5.6041 


124 


15.376 


1,906,624 


II. 1355 


4.9866 


177 


31,329 


5,545,233 


13.3041 


5.6147 


125 


15,625 


1,953,125 


II. 1803 


5 


178 


31.684 


5,639,752 


13.3417 


5.6252 


126 


15.876 


2,000,376 


11.2250 


5.0133 


179 


32,041 


5.735.339 


13.3791 


5.6357 


127 


16,129 


2,048,383 


11.2694 


5.0265 


180 


32,400 


5.832,000 


13.4164 


5.6462 


128 


16.384 


2,097,152 


11-3137 


5.0397 


181 


32,761 


5.929,741 


13.4536 


5.6567 


129 


16,641 


2,146,689 


11.3578 


5.0528 


182 


33.124 


6,028,568 


13.4907 


5.6671 


130 


16,900 


2,197,000 


II. 4018 


5.0658 


183 


33.489 


6,128,487 


13.5277 


5.6774 


131 


17.161 


2,248,091 


11.4455 


5.0788 


184 


33.856 


6,229,504 


13.5647 


5.6877 


132 


17,424 


2.299,968 


I I. 4891 


5-0916 


I8S 


34,225 


6,331,625 


13.6015 


5.6980 


133 


17.689 


2.352,637 


11.5326 


5.1045 


186 


34.596 


6,434,856 


13.6382 


5.7083 


134 


17,956 


2,406,104 


11-5758 


5.1172 


187 


34.969 


6,539,203 


13.6748 


5.7185 


135 


18,225 


2,460,375 


II. 6190 


5.1299 


188 


35.344 


6,644,672 


13.7113 


5.7287 


136 


18,496 


2,515,456 


II. 6619 


5. 1426 


189 


35.721 


6,751,269 


13-7477 


5.7388 


137 


18,769 


2.571,353 


11.7047 


5.1551 


190 


36.100 


6,859,000 


13.7840 


5.7489 


138 


19.044 


2,628,072 


11.7473 


5.1676 


191 


36,481 


6,967,871 


13.8203 


5.7590 


139 


19.321 


2,685,619 


11.7898 


5.1801 


192 


36,864 


7,077,888 


13.8564 


5.7690 


140 


19.600 


2.744,000 


11.8322 


5.1925 


193 


37.249 


7,189,057 


13.8924 


5.7790 


141 


19.881 


2,803,221 


11.8743 


5.2048 


194 


37.636 


7,301,384 


13.9284 


5.7890 


142 


20,164 


2,863,288 


I I. 9164 


5. 2171 


195 


38,025 


7,414,875 


13.9642 


5.7989 


143 


20.449 


2,924,207 


11-9583 


5. 2293 


196 


38,416 


7,529,536 


14 


5.8088 


144 


20,736 


2,985,984 


12 


5.2415 


197 


38,809 


7,645,373 


14.0357 


5.8186 


I4S 


21.025 


3,048,625 


12.0416 


5.2536 


198 


39.204 


7,762,392 


14.0712 


5.8285 


146 


21.316 


3,112,136 


12.0830 


5.2656 


199 


39.601 


7,880,599 


14.1067 


5.8383 


147 


21,609 


3.176,523 


12.1244 


5.2776 


200 


40.000 


8,000,000 


14.1421 


5.8480 


148 


21,904 


3,241.792 


12.1655 


5.2896 


201 


40,401 


8,120,601 


14.1774 


5.8578 


149 


22,201 


3.307.949 


12 2066 


5.3015 


202 


40,804 


8,242,408 


14.2127 


5.8675 


150 


22,500 


3,375,000 


12.2474 


5.3133 


203 


41,209 


8,365.427 


14.2478 


5.8771 


151 


22,801 


3,442,951 


12 . 2882 


5.3251 


204 


41,616 


8,489.664 


14.2829 


5.8868 



\ 



Table of Squares, Cubes, Square Roots and Cube Roots 49 



Table of Squares, Cubes, Square Roots and Cube Roots 
OF Numbers from i to iooo — {Continued) 



Square 


Cube 


Square 
root 


Cube 
root 


No. 


Square 


42,02s 


8,615,12s 


14.3178 


5.8964 


258 


66,564 


42,436 


8,741,816 


14.3527 


5.9059 


259 


67,081 


42,849 


8,869,743 


14.3875 


5. 9155 


260 


67,600 


43,264 


8,998,912 


14.4222 


5.9250 


261 


68,121 


43,681 


9,129,329 


14.4568 


5.9345 


262 


68,644 


44,icxD 


9,261,000 


14.4914 


5.9439 


263 


69,169 


44,521 


9.393,931 


14.5258 


5.9533 


264 


69,696 


44,944 


9.528,128 


14.5602 


5.9627 


265 


70,225 


45,369 


9.663,597 


14.5945 


5. 9721 


266 


70,756 


45,796 


9,800,344 


14.6287 


5.9814 


267 


71,289 


46,225 


9.938,375 


14.6629 


5.9907 


268 


7^,824 


46,656 


10,077,696 


14.6969 


6 


269 


72,361 


47,089 


10,218,313 


14.7309 


6.0092 


270 


72,900 


47,524 


10,360,232 


14.7648 


6.018s 


271 


73,441 


47,961 


10,503,459 


14.7986 


6.0277 


272 


73,984 


48.400 


10,648,000 


14.8324 


6.0368 


273 


74,529 


48,841 


10,793,861 


14.8661 


6.0459 


274 


75,076 


49,284 


10,941,048 


14.8997 


6.0550 


275 


75,625 


49,729 


11,089,567 


14.9332 


6.0641 


276 


76,176 


50,176 


11,239,424 


14.9666 


6.0732 


277 


76,729 


50,625 


11,390,62s 


15 


6.0822 


278 


77.284 


51,076 


11,543,176 


15.0333 


6.0912 


279 


77,841 


51,529 


11,697,083 


15.0665 


6.1002 


280 


78,400 


51,984 


11,852,352 


15.0997 


6.1091 


281 


78,961 


52,441 


12,008,989 


15.1327 


6.1180 


282 


79,524 


52,900 


12,167,000 


15.1658 


6.1269 


283 


80,089 


53,361 


12,326,391 


15.19S7 


6.1368 


284 


80,656 


53,824 


12,487,168 


15.2315 


6.1446 


285 


81, 22s 


54,289 


12,649,337 


15.2643 


6.IS34 


286 


81,796 


54,756 


12,812,904 


15.2971 


6.1622 


287 


82,369 


55.225 


12,977,875 


15.3297 


6.1710 


288 


82,944 


55,696 


13,144,256 


15.3623 


6.1797 


289 


83,521 


56,169 


13,312,053 


15.3948 


6.188S 


290 


84,100 


56,644 


13,481,272 


15.4272 


6.1972 


291 


84,681 


57,121 


13,651,919 


15.4596 


6.2058 


292 


85,264 


57,600 


13,824,000 


15.4919 


6.2145 


293 


85,849 


58,081 


13,997.521 


15.5242 


6.2231 


294 


86,436 


58,564 


14,172,488 


15.5563 


6.2317 


295 


87,025 


59,049 


14,348,907 


15.588s 


6 . 2403 


296 


87,616 


59,536 


14,526,784 


15.6205 


6.2488 


297 


88,209 


60,025 


14,706,125 


15.6525 


6.2573 


298 


88,804 


60,516 


14,886,936 


15.6844 


6.2658 


299 


89,401 


61,009 


15,069,223 


15.7162 


6.2743 


300 


90,000 


61,504 


15,252.992 


15.7480 


6.2828 


301 


90,601 


62,001 


15,438,249 


15.7797 


6.2912 


302 


91,204 


62,500 


15,625,000 


1S.8114 


6.2936 


303 


91,809 


63,001 


15,813,251 


15.8430 


6.3080 


304 


92,416 


63,504 


16,003,008 


15.8745 


6.3164 


305 


93,025 


64,009 


16,194,277 


15.9060 


6.3247 


306 


93,636 


64,516 


16,387,064 


15.9374 


6.3330 


307 


94,249 


65,025 


16,581,375 


15.9687 


6.3413 


308 


94,864 


65,536 


16,777,216 


16 V 


6.3496 


309 


95,481 


66,049 


16,974,593 


16.0312 


6.3579 


310 


96,100 



Cube 



17,173,512 
17,373,979 
17,576,000 
17,779,581 
17,984,728 
18,191,447 
18,399,744 
18,609,625 
18,821,096 
19,034,163 
19,248,832 
19.46s. 109 
19.683,000 
19,902,511 
20,123,648 
20,346,417 
20,570,824 
20,796,875 
21,024,576 
21,253,933 
21,484,952 
21,717,639 
21,952,00c 
22,188,041 
22,425,768 
22,665,187 
22,906,304 
23,149,125 
23,393,656 
23,639,903 
23,887,872 
24,137,569 
24,389,000 
24,642,171 
24,897,088 
25,153,757 
25,412,184 
25,672,375 
25,934,336 
26,198,073 
26,463,592 
26,730,899 
27,000,000 
27,270,901 
27,543,608 
27,818,127 
28,094,464 
28,372,625 
28,652,616 
28,934,443 
29,218,112 
29.503,629 
29,791,000 



Square 
root 



16.0624 

16.0935 

16.1245 

16.1555 

16.1864 

16.2173 

16.2481 

16.2788 

16.3095 

16.3401 

16.3707 

16.4012 

16.4317 

16.4621 

16 . 4924 

16.5227 

16.5529 

16.5831 

.16.6132 

16.6433 

16.6733 

16.7033 

16.7332 

16,7631 

16.7929 

16.8226 

16.8523 

16.8819 

16.9115 

16.9411 

16.9706 

I? 

17.0294 

17.0587 

17.0880 

17.1172 

17.1464 

17.1756 

17.2047 

17 . 2337 

17.2627 

17.2916 

17. 320s 

17.3494 

17.3781 

17.4069 

17.4356 

17 . 4642 

17.4929 

17.5214 

17-5499 

17.5784 

17.6068 



50 



Mathematical Tables 



Table of Squares, Cubes, Square Roots and Cube Roots 
OF Numbers from i to iooo — {Continued) 



No. 


Square 


Cube 


Square 
root 


Cube 
root 


No. 
364 


Square 


Cube 


Square 
root 


Cube 
root 


311 


96.721 


30,080,231 


17.6352 


6.7752 


132,496 


48,228,544 


19.0788 


7.1400 


312 


97.344 


30,371,328 


17.663s 


6.7824 


365 


133,225 


48.627,125 


19.1050 


7.1466 


313 


97,969 


30,664.297 


17.6918 


6.7897 


366 


133,956 


49,027,896 


19.1311 


7.IS3I 


314 


98.596 


30,959.144 


17.7200 


6.7969 


367 


134.689 


49,4.30.863 


19.1572 


7.1596 


31S 


99,225 


31,255.875 


17.7482 


6.8041 


368 


135.424 


49.836,032 


19.1833 


7.1661 


316 


99.856 


31,554.496 


17.7764 


6.8113 


369 


136,161 


50,243,409 


19.2094 


7.1726 


317 


100,489 


31. 85s .013 


17.8045 


6.8185 


370 


136,900 


50,653,000 


19.2354 


7.1791 


318 


101,124 


32,157,432 


17.8326 


6.8256 


371 


137,641 


51,064,811 


19.2614 


7.1855 


319 


101,761 


32,461,759 


17.8606 


6.8328 


372 


138,384 


51,478,848 


19.2873 


7.1920 


320 


102,400 


32,768,000 


17.8885 


6.8399 


373 


139,129 


51 .895.117 


19.3132 


7.1984 


321 


103,041 


33.076,161 - 


17.9165 


6.8470 


374 


139.876 


52,313.624 


19.3391 


7.2048 


322 


103,684 


33.386,248 


17.9444 


6.8541 


375 


140,625 


52,734.375 


19.3649 


7.2112 


323 


104,329 


33.698,267 


17.9722 


6.8612 


376 


141.376 


53.157.376 


19-3907 


7.2177 


324 


104,976 


34.012,224 


18 


6.8683 


377 


142,129 


53.582,633 


19.4165 


7.2240 


325 


105,625 


34,328,125 


18.0278 


6.8753 


378 


142,884 


54.010,152 


19.4422 


7.2304 


326 


106.276 


34.645.976 


18.0555 


6.8824 


379 


143.641 


54.439.939 


19.4679 


7-2368 


327 


106,929 


34.965.783 


18.0831 


6.8894 


380 


144.400 


54.872,000 


19.4936 


7.2432 


328 


107,584 


35,287.552 


18. I 108 


6.8964 


381 


145,161 


55.306,341 


19.5192 


7.2495 


329 


108,241 


35.611,289 


18.1384 


6.9034 


382 


145.924 


55.742.968 


19.5448 


7.2558 


330 


108,900 


35,937.000 


18. 1659 


6.9104 


383 


146,689 


56.181,887 


19.5704 


7.2622 


331 


109,561 


36,264,691 


18.1934 


6.9174 


384 


147,456 


56,623,104 


19-5959 


7.2685 


332 


110,224 


36,594.368 


18.2209 


6.9244 


385 


148,225 


57,066,625 


19-6214 


7.2748 


333 


110,889 


36,926,037 


18.2483 


6.9313 


386 


148,996 


57.512.456 


19.6469 


7.2811 


334 


111,556 


37.259.704 


18.2757 


6.9382 


387 


149.769 


57.960,603 


19-6723 


7.2874 


335 


112,225 


37.595.375 


18.3030 


6.9451 


388 


150,544 


58,411,072 


19.6977 


7-2936 


336 


112,896 


37.933,056 


18.3303 


6.9521 


389 


151. 321 


58,863,869 


19-7231 


7.2999 


337 


113,569 


38.272,753 


18.3576 


6.9589 


390 


152,100 


59.319.000 


19.7484 


7.3061 


338 


114,244 


38,614,472 


18.3848 


6.9658 


391 


152,881 


59,776,471 


19.7737 


7.3124 


339 


114,921 


38,958.219 


18.4120 


6.9727 


392 


153.664 


60,236,288 


19.7990 


7.3186 


340 


115,600 


39-304,000 


18.4391 


6.9795 


393 


154.449 


60,698,457 


19.8242 


7.3248 


341 


116,281 


39.651. 821 


18.4662 


6.9864 


394 


155.236 


61,162,984 


19.8494 


7.3310 


342 


116,964 


40,001,688 


18.4932 


6.9932 


395 


156,025 


61,629,875 


19.8746 


7.3372 


343 


117,649 


40,353.607 


18.5203 


7 


396 


156,816 


62,099,136 


19-8997 


7.3434 


344 


118,336 


40,707,584 


18.5472 


7.0068 


397 


157,609 


62,570,773 


19.9249 


7.3496 


345 


119,025 


41,063,625 


18.5742 


7.0136 


398 


158,404 


63,044,792 


19-9499 


7-3558 


346 


119,716 


41,421,736 


18.6011 


7.0203 


399 


159,201 


63,521,199 


19.9750 


7-3619 


347 


120,409 


41,781,923 


18.6279 


7.0271 


400 


160,000 


64,000,000 


20 


7-3681 


348 


121,104 


42,144,192 


18.6548 


7.0338 


401 


160,801 


64,481,201 


20.0250 


7.3742 


349 


121,801 


42,508,549 


18.6815 


7.0406 


402 


161,604 


64,964,808 


20.0499 


7.3803 


350 


122,500 


42,875.000 


18.7083 


7.0473 


403 


162,409 


65,450,827 


20.0749 


7.3864 


351 


123,201 


43.243.551 


18.7350 


7.0540 


404 


163,216 


65,939,264 


20.0998 


7.3925 


352 


123,904 


43.614,208 


18.7617 


7.0607 


405 


164,025 


66,430,125 


20.1246 


7.3986 


353 


124,609 


43,986,977 


18.7883 


7.0674 


406 


164,836 


66,923,416 


20.1494 


7.4047 


354 


125,316 


44,361,864 


18.8149 


7.0740 


407 


165,649 


67,419,143 


20.1742 


7.4108 


355 


126,025 


44,738,875 


18.8414 


7.0807 


408 


166,464 


67,917,312 


20.1990 


7.4169 


356 


126,736 


45.118,016 


18.8680 


7.0873 


409 


167,281 


68,417,929 


20.2237 


7.4229 


357 


127,449 


45,499,293 


18.8944 


7.0940 


410 


168,100 


68,921,000 


20.2485 


7.4290 


358 


128,164 


45,882,712 


18.9209 


7.1006 


411 


168,921 


69,426,531 


20.2731 


7.4350 


359 


128,881 


46,268,279 


18.9473 


7 . 1072 


412 


169,744 


69,934,528 


20.2978 


7.4410 


360 


129.600 


46,656,000 


18.9737 


7.1138 


413 


170,569 


70,444,997 


20.3224 


7.4470 


361 


130,321 


47,045,881 


19 


7 . 1204 


414 


171,396 


70,957,944 


20.3470 


7.4530 


362 


131,044 


47,437,928 


19.0263 


7.1269 


415 


172,225 


71,473.375 


20.3715 


7.4590 


363 


131,769 


47.832,147 


19.0526 


7.1335 


416 


173,056 


71,991,296 


20.3961 


7.4650 



Table of Squares, Cubes, Square Roots and Cube Roots 51 



Table of Squares, Cubes, Square Roots and Cube Roots 
OF Numbers from i to iooo — {Continued) 



No. 


Square 


Cube 


Square 
root 


Cube 
root 


No. 


Square 


Cube 


Square 
root 


Cube 
root 


417 


173.889 


72,511,713 


20.4206 


7.4710 


470 


220,900 


103,823,000 


21.6795 


7.7750 


418 


174,724 


73,034,632 


20.4550 


7.4770 


471 


221,841 


104,487,111 


21.702s 


7.7805 


419 


175,561 


73,560,059 


20.469s 


7.4829 


472 


222,784 


105,154,048 


21.7256 


7.7860 


420 


176,400 


74,088,000 


20.4939 


7.4889 


473 


223,729 


105,823,817 


21.7486 


7.791S 


421 


177,241 


74,618,461 


20. s 183 


7.4948 


474 


224,676 


106,496,424. 


21.7715 


7.7970 


422 


178,084 


75,151.448 


20.5426 


7.5007 


475 


225,625 


107,171.875 


21.7945 


7 8025 


423 


178,929 


75.686,967 


20.S670 


7.5067 


476 


226,576 


107,850,176 


21.8174 


7.8079 


424 


179.776 


76,225,024 


20.5913 


7.5126 


477 


227.529 


108,531,333 


21.8403 


7.8134 


42s 


180,62s 


76,765,625 


20.6155 


7.S185 


478 


228,484 


109,215,352 


21.8632 


7.8188 


426 


181,476 


77.308,776 


20.6398 


7.5244 


479 


229,441 


109,902,239 


21.8861 


7.8243 


427 


182,329 


77.854.483 


20.6640 


7.5302 


480 


230,400 


110,592,000 


21.9089 


7.8297 


428 


183,184 


78,402,752 


20.6882 


7.5361 


481 


231,361 


111,284,641 


21.9317 


7.8362 


429 


184,041 


78,953,589 


20.7123 


7.5420 


482 


232,324 


111,980,168 


21.9545 


7.8406 


430 


184,900 


79,507,000 


20.7364 


7.5478 


483 


233,289 


112,678,587 


21.9773 


7.8460 


431 


185.761 


80,062,991 


20.760s 


7.5537 


484 


234,256 


113,379.904 


22 


7.8514 


432 


186,624 


80,621,568 


20.7846 


7.5595 


485 


235.22s 


114.084,12s 


22.0227 


7.8568 


433 


187,489 


81,182,737 


20.8087 


7.5654 


486 


236,196 


114.791,256 


22.0454 


7.8622 


434 


188,356 


81,746,504 


20.8327 


7.5712 


487 


237.169 


115,501,303 


22.0681 


7.8676 


435 


189,225 


82,312,875 


20.8567 


7.5770 


488 


238,144 


116,214,272 


22.0907 


7.8730 


436 


190,096 


82,881,856 


20.8806 


7.5828 


489 


239.121 


116,930,169 


22.1133 


7.8784 


437 


190,969 


83,453.453 


20.9045 


7.5886 


490 


240,100 


117,649,000 


22.1359 


7.8837 


438 


191,844 


84,027,672 


20.9284 


7.5944 


491 


241 -,081 


118,370,771 


22.158s 


7.8891 


439 


192,721 


84,604,519 


20.9523 


7.6001 


492 


242,064 


119,095,488 


22.1811 


7.8944 


440 


193,600 


85,184,000 


20.9762 


7.6059 


493 


243,049 


119,823,157 


22.2036 


7.8998 


441 


194,481 


85,766,121 


21 


7.6117 


494 


244,036 


120,553,784 


22.2261 


7.9051 


442 


195.364 


86,350,888 


21.0238 


7.6174 


495 


245,025 


121,287,37s 


22.2486 


7.9105 


443 


196,249 


86,938,307 


21.0476 


7.6232 


496 


246,016 


122,023,936 


22.2711 


7.9158 


444 


197.136 


87,528,384 


21.0713 


7.6289 


497 


247,009 


122,763,473 


22.2935 


7.9211 


445 


198,025 


88,i2i,i2S 


21.0950 


7.6346 


498 


248,004 


123,505,992 


22.3159 


7.9264 


446 


198,916 


88,716,536 


21.1187 


7.6403 


499 


249,001 


124,251,499 


22.3383 


7.9317 


447 


199.809 


89,314,623 


21 . 1424 


7.6460 


500 


250,000 


125,000,000 


22.3607 


7.9370 


448 


200,704 


89,915,392 


21.1660 


7.6517 


SOI 


251,001 


125,751,501 


22.3830 


7.9423 


449 


201,601 


90,518,849 


21 . 1896 


7.6574 


S02 


252,004 


126,506,008 


22.4054 


7.9476 


450 


202,500 


91,125,000 


21.2132 


7.6631 


503 


253.009 


127,263,527 


22.4277 


7.9528 


451 


203,401 


91,733,851 


21.2368 


7.6688 


S04 


254,016 


128,024,064 


22.4499 


7.9581 


452 


204,304 


92,345,408 


21.2603 


7.6744 


505 


255,025 


128,787,62s 


22.4722 


7.9634 


453 


205,209 


92,959.677 


21.2838 


7.6801 


506 


256,036 


129,554,216 


22.4944- 


7.9686 


454 


206,116 


93.S76.664 


21.3073 


7.6857 


507 


257,049 


130,323,843 


22.S167 


7.9739 


455 


207,02s 


94.196.37S 


21.3307 


7.6914 


S08 


258,064 


131,096,512 


22.5389 


7.9791 


456 


207,936 


94,818,816 


21.3542 


7.6970 


509 


259,081 


131,872,229 


22.5610 


7.9843 


457 


208,849 


95,443,993 


21.3776 


7.7026 


510 


260,100 


132,651,000 


22.5832 


7.9896 


458 


209,764 


96,071,912 


21.4009 


7.7082 


Sii 


261,121 


133,432,831 


22.6053 


7.9948 


459 


210,681 


96,702,579 


21.4243 


7.7138 


512 


262,144 


134,217,728 


22 . 6274 


8 


460 


211,600 


97,336,000 


21.4476 


7.7194 


513 


263,169 


135,005,697 


22.6495 


8.0052 


461 


212,521 


97,972,181 


21.4709 


7.7250 


514 


264,196 


135,796,744 


22.6716 


8.0104 


462 


213,444 


98,611,128 


21.4942 


7.7306 


51S 


265,225 


136,590,875 


22.6936 


8.0156 


463 


214,369 


99,252.847 


21.5174 


7.7362 


516 


266,256 


137,388,096 


22.7156 


8.0208 


464 


215,296 


99,897,344 


21 . 5407 


7.7418 


517 


267,289 


138,188,413 


22.7376 


8.0260 


465 


216,22s 


ioo,S44.62S 


21.5639 


7.7473 


518 


268,324 


138,991,832 


22.7596 


8.0311 


466 


217,156 


101,194,696 


21 . 5870 


7.7529 


519 


269,361 


139,798,359 


22.7816 


8.0363 


467 


218,089 


101,847,563 


21 . 6102 


7.7584 


520 


270,400 


140,608,000 


22.8035 


8.041S 


468 


219,024 


102,503,232 


21.6333 


7.7639 


521 


271,441 


141,420,761 


22.8254 


8.0466 


469 


219,961 


103,161,709 


21.6564 


7.7695 


522 


272,484 


'142,236,648 


22.8473 


8.0517 



52 



Mathematical Tables 



Table of Squares, Cubes, Square Roots and Cube Roots 
OF Numbers from i to iooo — {Continued) 



No. 


Square 


Cube 


Square 
root 


Cube 
root 


No. 


Square 


Cube 


Square 
root 


Cube 
root 


523 


273.529 


143,055.667 


22.8692 


8.0569 


576 


331,776 


191,102,976 


24 


8.3203 


524 


274,576 


143,877,824 


22 . 8910 


8.0620 


577 


332,929 


192,100,033 


24.0208 


8.3251 


525 


275,62s 


144,703.125 


22.9129 


8.0671 


578 


334,084 


193.100,552 


24.0416 


8.3300 


526 


276,676 


145.531,576 


22.9347 


8.0723 


579 


335,241 


194,104,539 


24.0624 


8.3348 


527 


277,729 


146,363,183 


22.9565 


8.0774 


580 


336,400 


195,112,000 


24.0832 


8.3396 


528 


278,784 


147,197,952 


22.9783 


8.0S25 


581 


337,561 


196,122,941 


24.1039 


8.3443 


529 


279,841 


148,035,889 


23 


8.0876 


582 


338,724 


197,137,368 


24.1247 


8.3491 


530 


280,900 


148,877,000 


23.0217 


8.0927 


583 


339,889 


198.155,287 


24.1454 


8.3539 


531 


281,961 


149,721,291 


23.0434 


8.0978 


584 


341.056 


199.176,704 


24.1661 


8.3587 


532 


283,024 


150,568,768 


23.0651 


8.1028 


585 


342,225 


200,201,625 


24.1868 


8.3634 


533 


284,089 


151,419,437- 


23.0868 


8.1079 


586 


343.396 


201,230,056 


24.2074 


8.3682 


534 


285,156 


152.273,304 


23.1084 


8. I 130 


587 


344,569 


202,262,003 


24.2281 


8.3730 


535 


286,225 


153,130,375 


23.1301 


8.1180 


588 


345,744 


203,297,472 


24.2487 


8.3777 


536 


287,296 


153,990,656 


23.1517 


8.1231 


589 


346,921 


204,336,469 


24 . 2693 


8.3825 


537 


288,369 


154,854,153 


23.1733 


8.1281 


590 


348,100 


205,379-000 


24.2899 


8.3872 


538 


289,444 


155,720,872 


23.1948 


8.1332 


591 


349.281 


206,425,071 


24.3105 


8.3919 


539 


290,521 


156,590,819 


23.2164 


8.1382 


592 


350,464 


207,474,688 


24.3311 


8.3967 


S40 


291,600 


157,464,000 


23.2379 


8.1433 


593 


351,649 


208,526,857 


24.3516 


8.4014 


541 


292,681 


158,340,421 


23.2594 


8.1483 


594 


352,836 


209,584,584 


24.3721 


8.4061 


542 


293,764 


159,220,088 


23.2809 


8.1533 


595 


354,025 


210,644,875 


24.3926 


8.4108 


543 


294,849 


160,103,007 


23.3024 


8.1583 


596 


355,216 


211,708,736 


24.4131 


8.4155 


544 


295,936 


160,989,184 


23.3238 


8.1633 


597 


356,409 


212,776,173 


24.4336 


8.4202 


545 


297,02s 


161,878,625 


23.3452 


8.1683 


598 


357,604 


213,847.192 


24.4540 


8.4249 


546 


298.116 


162,771,336 


23.3666 


8.1733 


599 


358,801 


214.921,799 


24.4745 


8.4296 


547 


299.209 


163.667,323 


23.3880 


8.1783 


600 


360,000 


216,000,000 


24.4949 


8.4343 


548 


300,304 


164,566,592 


23.4094 


8.1833 


601 


361,201 


217,081,801 


24.5153 


8.4390 


549 


301,401 


165,469,149 


23.4307 


8.1882 


602 


362,404 


218,167,208 


24.5357 


8.4437 


550 


302,500 


166,375,000 


23.4521 


8.1932 


603 


363,609 


219,256,227 


24.5561 


8.4484 


551 


303,601 


167,284,151 


23.4734 


8.1982 


604 


364,816 


220,348,864 


24.5764 


8.4530 


552 


304,704 


168,196,608 


23.4947 


8 . 2031 


605 


366,025 


221,445,125 


24.5967 


8.4577 


553 


305,809 


169,112,377 


23.5160 


8 . 2081 


606 


367.236 


222,545.016 


24.6171 


8.4623 


554 


306,916 


170,031,464 


23.5272 


8.2130 


607 


368,449 


223,648,543 


24.6374 


8.4670 


555 


308,025 


170,953,875 


23.5584 


8 . 2180 


608 


369,664 


224,755,712 


24.6577 


8.4716 


556 


309,136 


171,879,616 


23.5797 


8 . 2229 


609 


370,881 


225,866,529 


24.6779 


8.4763 


557 


310,249 


172,808,693 


23.6008 


8.2278 


610 


372,100 


226,981,000 


24.6982 


8.4809 


558 


311,364 


173,741,112 


23 . 6220 


8.2327 


611 


373,321 


228,099,131 


24.7184 


8.4856 


559 


312.481 


174,676,879 


23.6432 


8.2377 


612 


374,544 


229,220,928 


24.7386 


8.4902 


56o 


313,600 


175.616,000 


23.6643 


8.2426 


613 


375,769 


230,346,397 


24.7588 


8.4948 


561 


314.721 


176.558,481 


23.6854 


8.2475 


614 


376,996 


231,475,544 


24.7790 


8.4994 


562 


31S.844 


177.504,328 


23.7065 


8.2524 


61S 


378,22s 


232,608,375 


24.7992 


8.5040 


563 


316,969 


178,453,547 


23.7276 


8.2573 


616 


379,456 


233,744,896 


24.8193 


8.5086 


564 


318,096 


179,406,144 


23.7487 


8.2621 


617 


380,689 


234,885,113 


24.8395 


8.5132 


565 


319,225 


180,362,125 


23.7697 


8.2670 


618 


381,924 


236,029,032 


24.8596 


8.5178 


566 


320,356 


181,321,496 


23.7908 


8.2719 


619 


383,161 


237,176,659 


24.8797 


8.5224 


567 


321,489 


182,284.263 


23.8118 


8.2768 


620 


384,400 


238,328,000 


24.8998 


8.5270 


568 


322,624 


183,250,432 


23.8328 


8.2816 


621 


385,641 


239.483,061 


24.9199 


8.5316 


569 


323,761 


184,220,009 


23.8537 


8.2865 


622 


386,884 


240,641,848 


24.9399 


8.5362 


S70 


324.900 


185,193,000 


23.8747 


8.2913 


623 


388,129 


241,804,367 


24.9600 


8.5408 


571 


326,041 


186,169,411 


23.8956 


8.2962 


624 


389,376 


242,970,624 


24.9800 


8.5453 


572 


327,184 


187,149,248 


23.916s 


8.3010 


625 


390,625 


244,140,62s 


25 


8.5499 


573 


328,329 


188,132,517 


23.9374 


8.3059 


626 


391,876 


245,314.376 


25.0200 


8.5544 


574 


329.476 


189,119,224 


23.9583 


8.3107 


627 


393,129 


246,491.883 


25.0400 


8.5590 


S75 


330,625 


190,109,375 


23.9792 


8.3155 


628 


394,384 


247,673.152 


25.0590 


8.563s 



\ 

Table of Squares, Cubes, Square Roots and Cube Roots 53 



Table oe Squares, Cubes, Square Roots and Cube Roots 
or Numbers from i to iooo — (Continued) 



No. 


Square 


Cube 


Square 
root 


Cube 
root 


No. 


Square 


Cube 


Square 
root 


Cube 
root 


629 


395,641 


248,858,189 


25.0799 


8.5681 


682 


465.124 


317,214.568 


26.1151 


8.8023 


630 


396,900 


250,047,000 


25.0998 


8.5726 


683 


466,489 


318,611,987 


26.1343 


8 


8066 


631 


398,161 


251,239.591 


25.1197 


8.5772 


684 


467.856 


320,013,504 


26.1534 


8 


8109 


632 


399.424 


252,435.968 


25 . 1396 


8.5817 


685 


469.225 


321,419.125 


26.1725 


8 


8152 


633 


400,689 


253.636,137 


25.1595 


8.5862 


686 


470,596 


322,828,856 


26.1916 


8 


8194 


634 


401,956 


254,840,104 


25 . 1794 


8.5907 


687 


471,969 


324,242,703 


26.2107 


8 


8237 


63s 


403,225 


256,047.875 


25.1992 


8.5952 


688 


473,344 


325,660,672 


26 . 2298 


8 


8280 


636 


404,496 


257,259.456 


25.2190 


8.5997 


689 


474.721 


327,082,769 


26.2488 


8 


8323 


637 


405,769 


258,474,853 


25 . 2389 


8.6043 


690 


476,100 


328,509,000 


26.2679 


8 


8366 


638 


407,044 


259,694,072 


25 . 2587 


8.6088 


691 


477,481 


329,939.371 


26.2869 


8 


8408 


639 


408,321 


260,917,119 


25.2784 


8.6132 


692 


478,864 


331,373.888 


26.3059 


8 


8451 


640 


409,600 


262,144,000 


25.2982 


8.6177 


693 


480,249 


332,812,557 


26.3249 


8 


8493 


641 


410.881 


263,374,721 


25.3180 


8.6222 


694 


481,636 


334.255.384 


26.3439 


8 


8536 


642 


412,164 


264,609,288 


25.3377 


8.6267 


695 


483,025 


335,702,375 


26.3629 


8 


8578 


643 


413,449 


265,847,707 


25.3574 


8.6312 


696 


484.416 


337,153.536 


26.3818 


8 


8621 


644 


414,736 


267,089,984 


25.3772 


8.6357 


697 


485,809 


338,608,873 


26.4008 


8 


8663 


645 


416.025 


268,336,125 


25.3969 


8.6401 


698 


487,204 


340,068,392 


26.4197 


8 


8706 


646 


417,316 


269,586,136 


25.4165 


8.6446 


699 


488,601 


341.532,099 


26.4386 


8 


8748 


647 


418,609 


270,840,023 


25.4362 


8.6490 


700 


490,000 


343.000,000 


26.4575 


8 


8790 


648 


419.904 


272,097,792 


25.4558 


8.6535 


701 


491.401 


344,472,101 


26.4764 


8 


8833 


649 


421,201 


273.359.449 


25.4755 


8.6579 


702 


492,804 


345.948,408 


26.4953 


8 


8875 


650 


422,500 


274,625,000 


25.4951 


8.6624 


703 


494,209 


347.428,927 


26.5141 


8 


8917 


651 


423,801 


275.894,451 


25.5147 


8.6668 


704 


495,616 


348,913,664 


26.5330 


8 


8959 


652 


425,104 


277,167,808 


25.5343 


8.6713 


705 


497,025 


350,402,625 


26.5518 


8 


9001 


653 


426,409 


278,445.077 


25.5539 


8.6757 


706 


498,436 


351,895,816 


26.5707 


8 


9043 


654 


427,716 


279.726,264 


25.5734 


8.6801 


707 


499-849 


353,393,243 


26.5895 


8 


9085 


655 


429,025 


281,011,375 


25.5930 


8.6845 


708 


501,264 


354,894,912 


26.6083 


8 


9127 


656 


430,336 


282,300,416 


25.6125 


8.6890 


709 


502,681 


356,400,829 


26.6271 


8 


9169 


657 


431.649 


283,593,393 


25.6320 


8.6934 


710 


504,100 


357.911.000 


26.6458 


8 


9211 


658 


432,964 


284,890,312 


25.6515 


8.6978 


711 


505,521 


359.425.431 


26.6646 


8 


9253 


659 


434,281 


286,191,179 


25.6710 


8.7022 


712 


506,944 


360,944,128 


26.6833 


8 


9295 


660 


435,600 


287,496,000 


25.6905 


8.7066 


713 


508,369 


362,467.097 


26 . 7021 


8 


9337 


661 


436,921 


288,804,781 


25.7099 


8.7110 


714 


509,796 


363.994.344 


26.7208 


8 


9378 


662 


438,244 


290,117,528 


25.7294 


8.7154 


71S 


511.225 


365,525,875 


26.7395 


8 


9420 


663 


439,569 


291,434,247 


25.7488 


8.7198 


716 


512,656 


367,061,696 


26.7582 


8 


9462 


664 


440,896 


292,754,944 


25.7682 


8.7241 


717 


514,089 


368,601,813 


26.7769 


8 


9503 


665 


442,225 


294,079,625 


25.7876 


8.7285 


718 


515.524 


370,146,232 


26.7955 


8 


9545 


666 


443,556 


295,408,296 


25.8070 


8.7329 


719 


516,961 


371.694.959 


26.8142 


8 


9587 


667 


444.889 


296,740,963 


25.8263 


8.7373 


720 


518,400 


373,248,000 


26.8328 


8 


9628 


668 


446,224 


298,077,632 


25.8457 


8.7416 


721 


519.841 


374.805,361 


26.8514 


8 


9670 


669 


447,561 


299.418,309 


25.8650 


8.7460 


722 


521,284 


375,367,048 


26.8701 


8 


971 1 


670 


448,900 


300,763,000 


25.8844 


8.7503 


723 


522,729 


377,933,067 


26.8887 


8 


9752 


671 


450,241 


302,111,711 


25.9037 


8.7547 


724 


524,176 


379.503.424 


26.9072 


8 


9794 


672 


451,584 


303,464.448 


25.9230 


8.7590 


72s 


525.625 


381,078,125 


26.9258 


8 


9835 


673 


452,929 


304,821,217 


25.9422 


8.7634 


726 


527.076 


382,657,176 


26.9444 


8 


9876 


674 


454,276 


306,182,024 


25.9615 


8.7677 


727 


528,529 


384,240,583 


26 . 9629 


8 


9918 


675 


455.625 


307,546,875 


25.9808 


8.7721 


728 


529.984 


385,828,352 


26.9815 


8 


9959 


676 


456,976 


308,915,776 


26 


8.7764 


729 


531.441 


387,420,489 


27 


9 




677 


458,329 


310,288,733 


26.0192 


8.7807 


730 


532,900 


389,017,000 


27.0185 


9 


0041 


678 


459,684 


311,665,752 


26.0384 


8.7850 


731 


534,361 


390,617,891 


27.0370 


9 


0082 


679 


461,041 


313,046,839 


26.0576 


8.7893I 


732 


535,824 


392,223,168 


27.0555 


9 


0123 


680 


462,400 


314,432,000 


26.0768 


a. 7937: 


733 


537,289 


393,832,837 


27.0740 


9 


0164 


681 


463,761 


315,821,241 


26.0960 


8.7980: 

! 


734 


538,756 


395,446,904 


27.0924 


9 


0205 



54 



Mathematical Tables 



Table of Squares, Cubes, Square Roots and Cube Roots 
OF Numbers from i to iooo — {Continued) 



No. 


Square 


Cube 


Square 
root 


Cube 
root 


No. 


Square 


Cube 


Square 
root 


Cube 
root 


733 


540,225 


397.065.375 


27.1109 


9.0246 


788 


620,944 


489.303.872 


28.0713 


9-2365 


736 


541.696 


398.688,256 


27.1293 


9.0287 


789 


622,521 


491.169,069 


28.0891 


9 


2404 


737 


543,169 


400,315.553 


27.1477 


9.0328 


790 


624,100 


493,039.000 


28.1069 


9 


2443 


738 


544.644 


401,947.272 


27.1662 


9.0369 


791 


625,681 


494,913,671 


28.1247 


9 


2482 


739 


546.121 


403.583.419 


27.1846 


9.0410 


792 


627,264 


496,793,088 


28.1425 


9 


2521 


740 


547.600 


405,224.000 


27 . 2029 


9.0450 


793 


628,849 


498,677,257 


28.1603 


9 


2560 


741 


549.081 


406,869,021 


27.2213 


9.0491 


794 


630,436 


500,566,184 


28.1780 


9 


2599 


742 


550,564 


408,518,488 


27.2397 


9.0532 


795 


632,025 


502,459,875 


28.1957 


9 


2638 


743 


552,049 


410,172,407 


27.2580 


9.0572 


796 


633,616 


504,358,336 


28.2135 


9 


2677 


744 


553,536 


411,830,784 


27.2764 


9.0613 


797 


635,209 


506,261,573 


28.2312 


9 


2716 


745 


555.025 


413,493,62s 


27.2947 


9.0654 


798 


636,804 


508,169,592 


28.2489 


9 


2754 


746 


556,516 


415.160,936 


27.3130 


9.0694 


799 


638,401 


510,082.399 


28.2666 


9 


2793 


747 


558,009 


416,832,723 


27.3313 


9.0735 


800 


640,000 


512,000,000 


28.2843 


9 


2832 


748 


559.504 


418,508,992 


27.3496 


9.077s 


801 


641,601 


513,922,401 


28.3019 


9 


2870 


749 


561,001 


420,189,749 


27.3679 


9.0816 


802 


643,204 


515,849,608 


28.3196 


9 


2909 


7SO 


562,500 


421,875,000 


27.3861 


9.0856 


803 


644,809 


517,781,627 


28.3373 


9 


2948 


751 


564.001 


423,564,751 


27.4044 


9.0896 


804 


646,416 


519,718,464 


28.3549 


9 


2986 


752 


565,504 


425,259,008 


27.4226 


9.0937 


805 


648,025 


521,660,125 


28.3725 


9 


302s 


753 


567.009 


426,957,777 


27.4408 


9.0977 


806 


649,636 


523,606,616 


28.3901 


9 


3063 


754 


568,516 


428,661,064 


27.4591 


9.1017 


807 


651,249 


525,557,943 


28.4077 


9 


3102 


755 


570.025 


430,368,875 


27.4773 


9.1057 


808 


652,864 


527,514.112 


28.4253 


9 


3140 


756 


571,536 


432,081,216 


27.4955 


9.1098 


809 


654,481 


529,475,129 


28.4429 


9 


3179 


757 


573.049 


433,798.093 


27.5136 


9.1138 


810 


656,100 


531,441,000 


28.4605 


9 


3217 


758 


574,564 


435,519,512 


27.5318 


9.1178 


811 


657,721 


533,411,731 


28.4781 


9 


325s 


759 


576,081 


437,245,479 


27.5500 


9.1218 


812 


659,344 


535,387,328 


28.4956 


9 


3294 


760 


577,600 


438,976,000 


27.5681 


9.1258 


813 


660,969 


537.367.797 


28.5132 


9 


3332 


761 


579,121 


440.71 1. 081 ■ 


27.5862 


9.1298 


814 


662,596 


539,353.144 


28.5307 


9 


3370 


762 


580,644 


442.450,728 


27.6043 


9.1338 


815 


664.225 


541,343.375 


28.5482 


9 


3408 


763 


582,169 


444,194,947 


27.6225 


9.1378 


816 


665,856 


543,338,496 


28.5657 


9 


3447 


764 


583,696 


445,943,744 


27.6405 


9.1418 


817 


667,489 


545,338,513 


28.5832 


9 


3485 


76s 


585,225 


447,697,125 


27.6586 


9.1458 


818 


669,124 


547,343,432 


28.6007 


9 


3523 


766 


586,756 


449,455,096 


27.6767 


9.1498 


819 


670,761 


549,353,259 


28.6182 


9 


3561 


767 


588,289 


451,217,663 


27.6948 


9.1537 


820 


672,400 


551,368.000 


28.6356 


9 


3599 


768 


589,824 


452,984,832 


27.7128 


9-1577 


821 


674,041 


553,387,661 


28.6531 


9 


3637 


769 


591,361 


454.756,609 


27.7308 


9.1617 


822 


675,684 


555,412,248 


28.6705 


9 


3675 


770 


592.900 


456.533,000 


27.74891 


9.1657 


823 


677,329 


557,441,767 


28.6880 


9 


3713 


771 


594,441 


458,314,011 


27.7669 


9.1696 


824 


678,976 


559,476,224 


28.7054 


9 


3751 


772 


595,984 


460,099,648 


27.7849 


9-1736 


825 


680,625 


561,515,62s 


28.7228 


9 


3789 


773 


597,529 


461,889,917 


27 . 8029 


9-1775 


826 


682,276 


563,559,976 


28.7402 


9 


3827 


774 


599.676 


463,684,824 


27.8209 


9-I815 


827 


683,929 


565,609.283 


28.7576 


9 


3865 


775 


600,625 


465,484,37s 


27.8388 


9-1855 


828 


685.584 


567,663,552 


28.7750 


9 


3902 


776 


602,176 


467,288.576 


27.8568 


9-1894 


829 


687,241 


569,722.789 


28.7924 


9 


3940 


777 


603.729 


469,097,433 


27.8747 


9-1933 


830 


688,900 


571,787,000 


28.8097 


9 


3978 


778 


605,284 


470,910,952 


27.8927 


9-1973 


831 


690,561 


573,856,191 


28.8271 


9 


4016 


779 


606,841 


472,729,139 


27.9106 


9.2012 


832 


692,224 


575,930,368 


28.8444 


9 


4053 


780 


608,400 


474,552,000 


27.9285 


9-2052 


833 


693,889 


578,009,537 


28.8617 


9 


4091 


781 


609,961 


476.379.541 


27.9464 


9.2091 


834 


695,556 


580.093,704 


28.8791 


9 


4129 


782 


611,524 


478.211,768 


27.9643 


9.2130 


835 


697,22s 


582,182,875 


28.8964 


9 


4166 


783 


613,089 


480,048,687 


27.9821 


9.2170 


836 


698,896 


584,277,056 


28.9137 


9 


4204 


784 


614,656 


481,890,304 


28 


9.2209 


837 


700,569 


586,376,253 


28.9310 


9 


4241 


785 


616,225 


483,736,625 


28.0179 


9.2248 


838 


702,244 


588,480,472 


28.9482 


9 


4279 


786 


617.796 


485,587,656 


28.0357 


9.2287 


839 


703,921 


590.589,719 


28.9655 


9 


4316 


787 


619,369 


487,443,403 


28.0535 


9.2326 


840 


705,600 


592,704,000 


28.9828 


9 


4354 



Table of Squares, Cubes, Square Roots and Cube Roots 55 



Table or Squares, Cxjbes, Square Roots and Cube Roots 
OF Numbers from i to iooo — {Continued) 



No. 


Square 


Cube 


Square 
root 


Cube 
root 


No. 


Square 


, Cube 


Square 
root 


Cube 
root 


841 


707,281 


594.823,321 


29 


3.4391 


894 


799,236 


714,516,984 


29.8998 


9.6334 


842 


708,964 


596,947,688 


29.0172 


3.4429 


895 


801,025 


716,917,375 


29.9166 


9.6370 


843 


710,649 


599,077,107 


29-0345 


3.4466 


896 


802,816 


719,323,136 


29.9333 


9.6406 


844 


712,336 


601,211,584 


29.0517 ( 


3.4503 


897 


804,609 


721,734,273 


29.9500 


9.6442 


84s 


714,025 


603,351,125 


29.0689 ( 


).454i 


898 


806,404 


724,150,792 


29.9666 


9.6477 


846 


715,716 


605,495,736 


29.0861 ( 


)-4578 


899 


808,201 


726,572,699 


29.9833 


9.6513 


847 


717.409 


607,645.423 


29.1033 c 


3.4615 


900 


810,000 


729,000,000 


30 


9.6549 


848 


719,104 


609,800,192 


29.1204 c 


^.4652 


901 


811,801 


731,432,701 


30.0167 


9.6585 


849 


720,801 


611,960,049 


29.1376 c 


^.4690 


902 


813,604 


733,870,808 


30.0333 


9.6620 


850 


722,500 


614,125,000 


29.1548 c 


).4727 


903 


815,409 


736,314,327 


30.0500 


9.6656 


851 


724,201 


616,295,051 


29.1719 c 


).4764 


904 


817,216 


738,763,264 


30.0666 


9.6692 


852 


725,904 


618,470,208 


29.1890 c 


).48oi 


905 


819,025 


741.217,625 


30.0832 


9.6727 


853 


727,609 


620,650,477 


29 . 2062 c 


).4838 


906 


820,836 


743,677,416 


30.0998 


9.6763 


854 


729,316 


622,835.864 


29.2233 c 


.4875 


907 


822,649 


746,142,643 


30.1164 


9-6799 


855 


731,025 


625,026,375 


29.2404 c 


).49I2 


908 


824,464 


748,613,312 


30.1330 


9.6834 


856 


732,736 


627,222,016 


29.2575 c 


.4949 


909 


826,281 


751,089,429 


30.1496 


9.6870 


857 


734.449 


629,422,793 


29.2746 c 


.4986 


910 


828,100 


753,571,000 


30.1662 


9.6905 


858 


736,164 


631,628,712 


29.2916 c 


.5023 


911 


829,921 


756,058,031 


30.1828 


9.6941 


859 


737.881 


633,839,779 


29.3087 c 


.5060 


912 


831,744 


758,550,528 


30.1993 


9.6976 


860 


739.600 


636,056,000 


29:3258 c 


.5097 


913 


833,569 


761,048,497 


30.2159 


9-7012 


861 


741.321 


638,277,381 


29.3428 c 


.5134 


914 


835,396 


763,551,944 


30.2324 


9.7047 


862 


743.044 


640,503,928 


29.3598 c 


.5171 


915 


837,225 


766,060,875 


30.2490 


9.7082 


863 


744.769 


642,735,647 


29.3769 c 


.5207 


916 


839.056 


768,575,296 


30.2655 


9.7118 


864 


746,496 


644,972,544 


29.3939 c 


.5244 


917 


840,889 


771.095.213 


30.2820 


9.7153 


86s 


748,225 


647,214,625 


29.4109 c 


.5281 


918 


842,724 


773 620,632 


30.2985 


9.7188 


866 


749.956 


649,461,896 


29.4279 c 


.5317 


919 


844.561 


776,151.559 


30.3150 


9.7224 


867 


751.689 


651,714,363 


29.4449 c 


.5354 


920 


846,400 


778,688,000 


30.3315 


9.7259 


868 


753,424 


653,972,032 


29.4618 c 


.5391 


921 


848,241 


781,229,961 


30.3480 


9.7294 


869 


755.161 


656,234,909 


29.4788 c 


• 5427 


922 


850,084 


783,777,448 


30.3645 


9.7329 


870 


756,900 


658,503,000 


29.4958 c 


.5464 


923 


851.929 


786,330,467 


30.3809 


9 7364 


871 


758,641 


660,776,311 


29.5127 c 


.5501 


924 


853.776 


788,889,024 


30.3974 


9.7400 


872 


760,384 


663,054,848 


29.5296 c 


.5537 


925 


855,625 


791,453,125 


30.4138 


9.7435 


873 


762,129 


665,338,617 


29.5466 c 


.5574 


926 


857,476 


794,022,776 


30.4302 


9.7470 


874 


763.876 


667,627,624 


29.5635 c 


.5610 


927 


859,329 


796,597,983 


30.4467 


9 -750s 


87s 


765.625 


669,921,875 


29.5804 c 


.5647 


928 


861,184 


799.178,752 


30.4631 


9.7540 


876 


767,376 


672,221,376 


29.5973 c 


.5683 


929 


863,041 


801,765,089 


30.479s 


9.7575 


877 


769,129 


674,526,133 


29.6142 c 


.5719 


930 


864,900 


804,357.000 


30.4959 


9.7610 


878 


770,884 


676,836,152 


29.6311 c 


■ 5756 


931 


866,761 


806,954,491 


30.5123 


9.7645 


879 


772,641 


679,151,439 


29.6479 c 


.5792 


932 


868,624 


809,557,568 


30.5287 


9.7680 


880 


774,400 


681,472,000 


29.664S c 


.5828 


933 


870,489 


812,166,237 


30.5450 


9.7715 


881 


776,161 


683,797,841 


29.6816 c 


.5865 


934 


872,356 


814,780,504 


30.5614 


9.7750 


882 


777.924 


686,128,968 


29.6985 c 


.5901 


935 


874,225 


817,400,375 


30.5778 


9.778S 


883 


779.689 


688,465,387 


29.7153 c 


.5937 


936 


876,096 


820,025,856 


30.5941 


9.7819 


884 


781,456 


690,807,104 


29.7321 c 


.5973 


937 


877,969 


822,656,953 


30.610S 


9.7854 


885 


783,225 


693,154,125 


29.7489 c 


.6010 


938 


879,844 


825,293,672 


30.6268 


9.7889 


886 


784.996 


695,506,456 


29.7658 c 


.6046 


939 


881,721 


827,936,019 


30.6431 


9.7924 


887 


786,769 


697,864,103 


29.7825 c 


).6o82 


940 


883,600 


830,584,000 


30.6594 


9.7959 


888 


788,544 


700,227,072 


29.7993 c 


).6ii8 


941 


885,481 


833,237,621 


30.6757 


9.7993 


889 


790,321 


702,595,369 


29.8161 c 


).6i54 


942 


887,364 


835.896,^88 


30 . 6920 


9.8028 


890 


792,100 


704,969,000 


29.8329 c 


).6i9o 


943 


889,249 


838,561,807 


30.7083 


9.8063 


891 


793.881 


707,347,971 


29 . 8496 c 


).6226 


944 


891,136 


841,232,384 


^0 7246 


9.8097 


892 


795,664 


709,732,288 


29.8664 < 


).6262 


945 


893,025 


843,908,625 


30.7409 


9.8132 


893 


797,449 


712,121,957 


29.8831 c 


).6298 


946 


894,916 


846,590,536 


30.7571 


9.8167 



56 



Mathematical Tables 



Table of Squares, Cubes, Square Roots and Cube Roots 
OF Numbers from i to iooo — {Continued) 



No. 


Square 


Cube 


Square 
root 


Cube 
root 


No. 

974 


Square 


Cube 


Square 
root 


Cube 
root 


947 


896,809 


849,278,123 


30.7734 


9 . 8201 


948.676 


924,010,424 


31.2090 c 


).9i26 


948 


898,704 


851,971.392 


30.7896 


9 . 8236 


975 


950.625 


926,859,375 


31 . 2250 ( 


).9i6o 


949 


900,601 


854.670,349 


30.8058 


9.8270 


976 


952,576 


929,714,176 


31.2410 ( 


).9i94 


950 


902,500 


857,375,000 


30.8221 


9.8305 


977 


954,529 


932,574.833 


31.2570 


J. 9227 


951 


904,401 


860,085,351 


30.8383 


9 8339 


978 


956,484 


935.441,352 


31.2730 


?.926i 


952 


906,304 


862,801,408 


30.854s 


9.8374 


979 


958,441 


938,313,739 


31.2890 


3.9295 


953 


908,209 


865,523,177 


30.8707 


9.8408 


980 


960,400 


941,192,000 


31.3050 


9.9329 


954 


910,116 


868,250,664 


30.8869 


9.8443 


981 


962,361 


944,076,141 


31.3209 


3.9363 


955 


912,02s 


870,983,875 


30.9031 


9.8477 


982 


964,324 


946,966,168 


31.3369 


9.9396 


9S6 


913,936 


873.722,816 


30.9192 


9.8511 


983 


966,289 


949,862,087 


31.3528 


9.9430 


957 


915,849 


876,467,493 


30.9354 


9.8546 


984 


968,256 


952,763,904 


31.3688 


9.9464 


958 


917,764 


879.217.912 


30. 9516 j 9. 8580 


985 


970,225 


955,671.625 


31.3847 


9.9497 


959 


919,681 


881,974,079 


30.9677 


9.8614 


986 


972,196 


958,585.256 


31 . 4006 


9.9531 


960 


921,600 


884,736',ooo 


30.9839 


9.8648 


987 


974,169 


961,504,803 


31.4166 


9.9565 


961 


923,521 


887,503,681 


31 


9.8683 


988 


976,144 


964,430,272 


31.432s 


9.9598 


962 


925,444 


890,277,128 


31.0161 


9.8717 


989 


978,121 


967,361,669 


31.4484 


9.9632 


963 


927.369 


893,056,347 


31-0322 


9.8751 


990 


980,100 


970,299,000 


31.4643 


9.9666 


964 


929,296 


895,841,344 


31.0483 


9.8785 


991 


982,081 


973,242,271 


31.4802 


9.9699 


965 


931,22s 


898,632,125 


31-0644 


9.8819 


992 


984.064 


976,191,488 


31 . 4960 


9.9733 


966 


933,156 


901,428,696 


31.0805 


9.8854 


993 


986,049 


979.146,657 


31.5119 


9.9766 


967 


935,089 


904,231,063 


31.0966 


9.8888 


994 


988,036 


982,107,784 


31.5278 


9.9800 


968 


937,024 


907,039.232 


31.1127 


9.8922 


995 


990,025 


985,074,875 


31.5436 


9.9833 


969 


938,961 


909,853.209 


31.1288l9.8956 


996 


992,016 


988,047,936 


31.5595 


9.9866 


970 


940,900 


912,673,000 


31.1448 


9.8990 


997 


994,009 


991,026,973 


31.5753 


9.9900 


971 


942,841 


915,498.611 


31.1609 


9.9024 


998 


996,004 


994,011,992 


31.5911 


9.9933 


972 


944,784 


918,330,048 


31 . 1769 


9.9058 


999 


998,001 


997,002,999 


31.6070 


9.9967 


973 


946,729 


921,167,317 


31.19299.9092 


IOOO 


1,000,000 


1,000,000,000 


31,6228 


10 



To find the square or cube of any whole number ending 
with ciphers. First, omit all the final ciphers. Take from the table the 
square or cube (as the case may be) of the rest of the number. To this 
square add twice as many ciphers as there were final ciphers in the original 
number. To the cube add three times as many as in the original number. 
Thus, for 90,5002, 9052 = 819,025. Add twice 2 ciphers, obtaining 
8,190,250,000. For 90,500^, 9053 = 741,217,625. Add 3 times 2 ci- 
phers, obtaining 741,217,625,000,000. 



I 



\ 

Table of Square Roots and Cube Roots of Numbers 57 



Table of Square Roots and Cube Roots or Numbers 

FROM 1000 TO 10,000 
No errors 



No. 


Sq. 


Cube 


No. 


Sq. 


Cube 


No. 


Sq. 


Cube 


No. 


Sq. 


Cube 


root 


root 


root 


root 


root 


root 


root 


root 


1005 


31.70 


10.02 


1270 


35.64 


10.83 


1535 


39.18 


11.54 


1800 


42.43 


12.16 


lOIO 


31 


78 


10.03 


1275 


35 


71 


10.84 


1540 


39-24 


11.55 


180S 


42.49 


12.18 


IOI5 


31 


86 


10.05 


1280 


35 


78 


10.86 


1545 


39.31 


11.56 


1810 


42.54 


12.19 


1020 


31 


94 


10.07 


1285 


35 


85 


10.87 


1550 


39.37 


11.57 


1815 


42.60 


12.20 


1025 


32 


02 


10.08 


1290 


35 


92 


10.89 


1555 


39.43 


11.59 


1820 


42.66 


12.21 


1030 


32 


09 


10.10 


1295 


35 


99 


10.90 


1560 


39 50 


11.60 


1825 


42.72 


12.22 


1035 


32 


17 


10.12 


1300 


36 


06 


10.91 


1565 


39.56 


II. 61 


1830 


42.78 


12.23 


1040 


32 


25 


10.13 


1305' 


36 


12 


10.93 


1570 


29.62 


11.62 


1835 


42.84 


12.24 


1045 


32 


33 


10.15 


1310 


36 


19 


10.94 


1575 


39.69 


11.63 


1840 


42.90 


12.25 


1050 


32 


40 


10.16 


131S 


36 


26 


10.96 


1580 


39.75 


II. 6s 


1845 


42.95 


12.26 


1055 


32 


48 


10.18 


1320 


36 


33 


10.97 


1585 


39.81 


11.66 


1850 


43.01 


12.28 


1060 


32 


56 


10.20 


132s 


36 


40 


10.98 


1590 


39-87 


11.67 


1855 


43.07 


12.29 


106s 


32 


63 


10.21 


1330 


36 


47 


II 


1595 


39.94 


11.68 


i860 


43.13 


12.30 


1070 


32 


71 


10.23 


1335 


36 


54 


II. 01 


1600 


40 


11.70 


1865 


43.19 


12.31 


1075 


32 


79 


10.24 


1340 


36 


61 


11.02 


1605 


40.06 


11.71 


1870 


43.24 


12.32 


1080 


32 


86 


10.26 


1345 


36 


67 


11.04 


1610 


40.12 


11.72 


187s 


43.30 


12.33 


108s 


32 


94 


10.28 


1350 


36 


74 


11.05 


1615 


40.19 


11.73 


1880 


43.36 


12.34 


1090 


33 


02 


10.29 


1355 


36 


81 


11.07 


1620 


40.25 


11.74 


188S 


43.42 


12.35 


1095 


33 


09 


10.31 


1360 


36 


88 


11.08 


1625 


40.31 


11.76 


1890 


43.47 


12.36 


HOC 


33 


17 


10.32 


1365 


36 


95 


11.09 


1630 


40.37 


11.77 


1895 


43.53 


12.37 


1 105 


33 


24 


10.34 


1370 


37 


01 


II. II 


1635 


40.44 


11.78 


1900 


43.59 


12.39 


IIIO 


33 


32 


10.3s 


1375 


37 


08 


II. 12 


1640 


•40.50 


11.79 


1905 


43.65 


12.40 


HIS 


33 


39 


10.37 


1380 


37 


15 


II. 13 


1645 


40.56 


11.80 


1910 


43.70 


12.41 


1 120 


33 


47 


10.38 


1385 


37 


22 


II. 15 


1650 


40.62 


11.82 


1915 


43.76 


12.42 


II25 


33 


54 


10.40 


1390 


37 


28 


II. 16 


1655 


40' 68 


11.83 


1920 


43.82 


12.43 


1 130 


33 


62 


10.42 


1395 


37 


35 


II. 17 


1660 


40.74 


11.84 


1925 


43.87 


12.44 


1 135 


33 


69 


10.43 


1400 


37 


42 


II. 19 


1665 


40.80 


II. 85 


1930 


43.93 


12. 45 


1 140 


33 


76 


10. 45 


1405 


37 


48 


11.20 


1670 


40.87 


11^86 


1935 


43.99 


12.46 


1 145 


33 


84 


10.46 


1410 


37 


55 


II. 21 


1675 


40.93 


11.88 


1940 


44.05 


12.47 


1 150 


33 


91 


10.48 


1415 


37 


62 


11.23 


1680 


40.99 


11.89 


1945 


44.10 


12.48 


1155 


33 


99 


10.49 


1420 


37 


68 


11.24 


1685 


41.05 


II . 90 


1950 


44.16 


12.49 


1160 


34 


06 


10.51 


1425 


37 


75 


11.25 


1690 


41. II 


II. 91 


1955 


44.22 


12.50 


1165 


34 


13 


10.52 


1430 


37 


82 


11.27 


1695 


41.17 


11.92 


i960 


44.27 


12.51 


1 170 


34 


21 


10. 54 


1435 


37 


88 


11.28 


1700 


41.23 


11.93 


1965 


44.33 


12.53 


1175 


34 


28 


10.55 


1440 


37 


95 


11.29 


1705 


41.29 


11.95 


1970 


44.38 


12.54 


1180 


34 


35 


10.57 


1445 


38 


01 


II. 31 


1710 


41.35 


11.96 


1975 


44.44 


12.55 


1 185 


34 


42 


10.58 


1450 


38 


08 


11.32 


1715 


41.41 


11.97 


1980 


44.50 


12.56 


1190 


34 


50 


10.60 


1455 


38 


14 


11.33 


1720 


41.47 


11.98 


1985 


44.55 


12.57 


1195 


34 


57 


10.61 


1460 


38 


21 


11.34 


172s 


41.53 


11.99 


1990 


44.61 


12.58 


1200 


34 


64 


10.63 


1465 


38 


28 


11.36 


1730 


41.59 


12 


1995 


44.67 


12.59 


1205 


34 


71 


10.64 


1470 


38 


34 


11.37 


1735 


41-65 


12.02 


2000 


44.72 


12.60 


1210 


34 


79 


10.66 


1475 


38 


41 


11.38 


1740 


41.71 


12.03 


2005 


44.78 


12.61 


1215 


34 


86 


10.67 


1480 


38 


47 


11.40 


1745 


41.77 


12.04 


2010 


44.83 


12.62 


1220 


34 


93 


10.69 


1485 


38 


54 


II. 41 


1750 


41.83 


12.05 


2015 


44.89 


12.63 


1225 


35 




10.70 


1490 


38 


60 


11.42 


1755 


41.89 


12.06 


2020 


44.94 


12.64 


1230 


35 


07 


10.71 


1495 


38 


67 


11.43 


1760 


41.95 


12.07 


2025 


45 


12.65 


1235 


35 


14 


10. "73 


1500 


38 


73 


11.45 


1765 


42.01 


12.09 


2030 


45 06 


12.66 


1240 


35 


21 


10.74 


150s 


38 


79 


11.46 


1770 


42.07 


12.10 


2035 


45.11 


12.67 


1245 


35 


28 


10.76 


1510 


38 


86 


11.47 


1775 


42.13 


12. II 


2040 


45. 17 


12.68 


1250 


35 


36 


10.77 


1515 


38 


92 


11.49 


1780 


42.19 


12.12 


2045 


45.22 


12.69 


I2SS 


35 


43 


10.79 


1520 


38 


99 


11.50 


1785 


42.25 


12.13 


2050 


45.28 


12.70 


1260 


35 


50 


10.80 


152s 


39 


05 


1I.5I 


1790 


42.31 


12.14 


2055 


45.33 


12.71 


1265 


35 


57 


10.82 


1530 


39 


12 


11.52 


1795 


42.37 


12.15 


2060 


45.39 


12.72 



58 



Mathematical Tables 



Table or Square Roots and Cube Roots of Numbers from 
looo to 10,000 — {Continued) 



No. 


Sq. 
root 


Cube 
root 


No. 


Sq. 
root 


Cube 
root 


No. 


Sq. 
root 


Cube 
root 


No. 


Sq. 
root 


Cube 
root 


2065 


45-44 


12.73 


2330 


48.27 


13.26 


2740 


52.35 


13-99 


3270 


57.18 


14.84 


2070 


45 


50 


12.74 


2335 


48 


32 


13 


27 


2750 


52.44 


14.01 


3280 


57.27 


14.86 


2075 


45 


55 


12.75 


2340 


48 


37 


13 


28 


2760 


52.54 


14-03 


3290 


57.36 


14.87 


2080 


45 


61 


12.77 


2345 


48 


43 


13 


29 


2770 


52.63 


14.04 


3300 


57.45 


14.89 


2085 


45 


66 


12.78 


2350 


48 


48 


13 


30 


2780 


52.73 


14.06 


3310 


57.53 


14.90 


2090 


45 


72 


12.79 


2355 


48 


53 


13 


30 


2790 


52.82 


14.08 


3320 


57.62 


14.92 


2095 


45 


77 


12.80 


2360 


48 


58 


13 


31 


2800 


52.92 


14.09 


3330 


57.71 


14.93 


2100 


45 


83 


12.81 


2365 


48 


63 


13 


32 


2810 


53.01 


14. II 


3340 


57.79 


14.9s 


210S 


45 


88 


12.82 


2370 


48 


68 


13 


33 


2820 


53. 10 


14.13 


3350 


57.88 


14.96 


21 10 


45 


93 


12.83 


2375 


48 


73 


13 


34 


2830 


53^20 


14.14 


3360 


57.97 


14.98 


2115 


45 


99 


12.84 


2380 


48 


79 


13 


35 


2840 


53^29 


14.16 


3370 


58.05 


14.99 


2120 


46 


04 


12.85 


2385 


48 


84 


13 


36 


2850 


53^39 


14.18 


3380 


58.14 


15.01 


2I2S 


46 


10 


12.86 


2390 


48 


89 


13 


37 


2860 


53^48 


14.19 


3390 


58.22 


15.02 


2130 


46 


15 


12.87 


2395 


48 


94 


13 


38 


2870 


53^57 


14.21 


3400 


58.31 


15.04 


2135 


46 


21 


12.88 


2400 


48 


99 


13 


39 


2880 


53^67 


14.23 


3410 


58.40 


15. OS 


2140 


46 


26 


12.89 


240s 


49 


04 


13 


40 


2890 


53^76 


14.24 


3420 


58.48 


15.07 


2145 


46 


31 


12.90 


2410 


49 


09 


13 


41 


2900 


53.85 


14.26 


3430 


58.57 


15 08 


2150 


46 


37 


12.91 


2415 


49 


14 


13 


42 


2910 


53.94 


14.28 


3440 


58.65 


15.10 


2155 


46 


42 


12.92 


2420 


49 


19 


13 


43 


2920 


54.04 


14.29 


3450 


58.74 


15. II 


2160 


46 


48 


12.93 


242s 


49 


24 


13 


• 43 


2930 


54.13 


14.31 


3460 


58.82 


15.12 


2165 


46 


53 


12.94 


2430 


49 


30 


13 


• 44 


2940 


54.22 


14.33 


3470 


58.91 


15.14 


2170 


46 


58 


12.95 


2435 


49 


35 


13 


• 45 


2950 


54.31 


14.34 


3480 


58.99 


15. IS 


2175 


46 


64 


12.96 


2440 


49 


40 


13 


.46 


2960 


54.41 


14.36 


3490 


59.08 


IS. 17 


2180 


46 


69 


12.97 


2445 


49 


45 


13 


• 47 


2970 


54 -50 


14-37 


3500 


59.16 


IS. 18 


2185 


46 


74 


12.98 


2450 


49 


50 


13 


• 48 


2980 


54.59 


14-39 


3510 


59.25 


15.20 


2190 


46 


80 


12.99 


2460 


49 


60 


13 


• 50 


2990 


54.68 


14.41 


3520 


59.33 


15.21 


219s 


46 


.85 


13 


2470 


49 


70 


13 


• 52 


3000 


54.77 


14.42 


3530 


59.41 


15.23 


2200 


46 


.90 


13.01 


2480 


49 


80 


13 


• 54 


3010 


54.86 


14.44 


3540 


59.50 


15.24 


2205 


46 


96 


13 02 


2490 


49 


90 


13 


• 55- 


3020 


54.95 


14.45 


3550 


59 58 


15.25 


2210 


47 


.01 


13.03 


2500 


50 




13 


57 


3030 


55.05 


14.47 


3560 


59.67 


15.27 


2215 


47 


06 


13.04 


2510 


50 


10 


13 


•59 


3040 


55.14 


14.49 


3570 


59-75 


15.28 


2220 


47 


.12 


13-05 


2520 


50 


20 


13 


61 


3050 


55.23 


14.50 


3580 


59-83 


IS. 30 


2225 


47 


• 17 


13.05 


2530 


50 


30 


13 


63 


3060 


55.32 


14.52 


3590 


59.92 


15.31 


2230 


47 


22 


13.06 


2540 


50 


40 


13 


64 


3070 


55.41 


14.53 


3600 


60 


15.33 


2235 


47 


28 


13.07 


2550 


50 


50 


13 


66 


3080 


.55.50 


14.55 


3610 


60.08 


IS. 34 


2240 


47 


.33 


13.08 


2560 


50 


60 


13 


68 


3090 


55.59 


14.57 


3620 


60.17 


IS. 35 


2245 


47 


.38 


13.09 


2570 


50 


70 


13 


70 


3100 


55.68 


14.58 


3630 


60.25 


15.37 


2250 


47 


43 


13.10 


2580 


50 


79 


13 


72 


3110 


55.77 


14.60 


3640 


60.33 


IS. 38 


2255 


47 


•49 


I3-II 


2590 


50 


89 


13 


73 


3120 


55.86 


14.61 


3650 


60.42 


15.40 


2260 


47 


54 


13- 12 


2600 


50 


99 


13 


75 


3130 


55.95 


14.63 


3660 


60.50 


IS. 41 


2265 


47 


59 


13.13 


2610 


51 


09 


13 


77 


3140 


56.04 


14.64 


3670 


60.58 


15.42 


2270 


47 


64 


13.14 


2620 


51 


19 


13 


79 


3150 


56.12 


14.66 


3680 


60.66 


15.44 


2275 


47 


70 


13.15 


2630 


51 


28 


13 


80 


3160 


56.21 


14.67 


3690 


60.75 


15^45 


2280 


47 


75 


13.16 


2640 


51 


38 


13 


82 


3170 


56.30 


14.69 


3700 


60.83 


15-47 


228s 


47 


80 


13.17 


2650 


51 


48 


13 


84 


3180 


56.39 


14.71 


3710 


60.91 


15.48 


2290 


47 


85 


13.18 


i 2660 


51 


58 


13 


86 


3190 


56.48 


14.72 


3720 


60.99 


IS. 49 


2295 


47 


91 


13.19 


2670 


51 


67 


13 


87 


3200 


56.57 


14.74 


3730 


61.07 


IS. SI 


2300 


47 


96 


13 -20 


2680 


51 


77 


13 


89 


3210 


56.66 


14.75 


3740 


61.16 


15.52 


2305 


48 


or 


13-21 


2690 


SI 


87 


13 


91 


3220 


56.75 


14.77 


3750 


61.24 


IS. 54 


2310 


48 


06 


13.22 


2700 


51 


96 


13 


92 


3230 


56.83 


14.78 


3760 


61.32 


IS.SS 


2315 


48 


II 


13.23 


2710 


52. 


06 


13 


94 


3240 


56.92 


14.80 


3770 


61.40 


15.56 


2320 


48 


17 


13.24 


2720 


52. 


15 


13 


9.6 


3250 


57- 01 


14.81 


3780 


61.48 


15. 58 


2325 


48 


22 


13.2s 


2730 


52. 


25 


13. 


98 


3260 


57.10 


14.83 


3790 


61.56 


15.59 



Table of Square Roots and Cube Roots 



59 



Table of Square Roots and Cube Roots of Numbers from 
looo to 10,000" — {Continued) 



No. 


Sq. 
root 


Cube 
root 


No. 


Sq. 
root 


Cube 
root 


No. 


Sq. 
root 


Cube 
root 


No. 


Sq. 
root 


Cube 
root 


3800 


61.64 


15.60 


4330 


65.80 


16.30 


4860 


69.71 


16.94 


S390 


73.42 


17.53 


3810 


61.73 


15.62 


4340 


65.88 


16.31 


4870 


69.79 


16.95 


5400 


73.48 


17.54 


3820 


61.81 


15.63 


4350 


65.9s 


16.32 


4880 


69.86 


16.96 


5410 


73.55 


17.55 


3830 


61.89 


15-65 


4360 


66.03 


16.34 


4890 


69.93 


16.97 


5420 


73-62 


17.57 


3840 


61.97 


15.66 


4370 


66.11 


16.35 


4900 


70 


16.98 


5430 


73-69 


17.58 


3850 


62.05 


15.67 


4380 


66. IS 


16.36 


4910 


70.07 


17 


5440 


73-76 


17.59 


3860 


62.13 


15.69 


4390 


66.26 


16.37 


4920 


70.14 


17.01 


5450 


73-82 


17.60 


3870 


62.21 


15.70 


4400 


66.33 


16.39 


4930 


70.21 


17.02 


5460 


73-89 


17.61 


3880 


62.29 


15.71 


4410 


66.41 


16.40 


4940 


70.29 


17.03 


5470 


73-96 


17.62 


3890 


62.37 


15.73 


4420 


66.48 


16.41 


4950 


70.36 


17.04 


5480 


74-03 


17-63 


3900 


62.45 


15.74 


4430 


66.56 


16.42 


4960 


70.43 


17. OS 


5490 


74.09 


17.64 


3910 


62.53 


15.75 


4440 


66.63 


16.44 


4970 


70.50 


17.07 


5500 


74.16 


17.65 


3920 


62.61 


15.77 


44SO 


66.71 


16.45 


4980 


70.57 


17.08 


5510 


74.23 


17.66 


3930 


62.69 


IS. 78 


4460 


66.78 


16.46 


4990 


70.64 


17.09 


5520 


74.30 


17.67 


3940 


62.77 


15.79 


4470 


66.86 


16.47 


Sooo 


70.71 


17.10 


5530 


74.36 


17.68 


3950 


62.85 


15.81 


4480 


66.93 


16.49 


5010 


70.78 


17. II 


5540 


74.43 


17.69 


3960 


62.93 


15.82 


4490 


67.01 


16.50 


5020 


70.85 


17.12 


S5SO 


74.50 


17.71 


3970 


63.01 


15.83 


4500 


67.08 


16.51 


5030 


70.92 


17.13 


5560 


74.57 


17.72 


3980 


63.09 


15.85 


4510 


67.16 


16.52 


5040 


70.99 


17.15 


5S70 


74.63 


17.73 


3990 


63. 17 


15.86 


4520 


67.23 


16.53 


5050 


71.06 


17.16 


5580 


74.70 


17.74 


4000 


63.25 


15.87 


4530 


67.31 


16.55 


5060 


71.13 


17.17 


5590 


74.77 


17.75 


4010 


63.32 


IS. 89 


4540 


67.38 


16.56 


5070 


71.20 


17.18 


5600 


74.83 


17.76 


4020 


63.40 


15.90 


4S50 


67.4s 


16.57 


5080 


71.27 


17.19 


5610 


74.90 


■17.77 


4030 


63.48 


15.91 


4560 


67.53 


16.58 


5090 


71.34 


17.20 


5620 


74.97 


17.78 


4040 


63.56 


15.93 


4570 


67.60 


16.59 


5100 


71.41 


17.21 


5630 


75.03 


17.79 


4050 


63.64 


15.94 


4580 


67.68 


16.61 


5110 


71.48 


17.22 


5640 


75.10 


17.80 


4060 


63.72 


IS. 95 


4590 


67.75 


16.62 


5120 


71.55 


17.24 


5650 


75.17 


17.81 


4070 


63.80 


15.97 


4600 


67.82 


16.63 


5130 


71.62 


17.25 


5660 


75.23 


17.82 


4080 


63.87 


IS. 98 


4610 


67.90 


16.64 


5140 


71.69 


17.26 


5670 


75.30 


17.83 


4090 


63.95 


15.99 


4620 


67.97 


16.66 


5150 


71.76 


17.27 


5680 


75.37 


17.84 


4100 


64.03 


16.01 


4630 


68.04 


16.67 


5160 


71.83 


17.28 


5690 


75.43 


17.85 


41T0 


64.11 


16.02 


4640 


68.12 


16.68 


5170 


71.90 


17.29 


S700 


75.50 


17.86 


4120 


64.19 


16.03 


4650 


68.19 


16.69 


5180 


71.97 


17.30 


5710 


75.56 


17.87 


4130 


64.27' 


16.04 


4660 


68.26 


16.70 


5190 


72.04 


17.31 


S720 


75.63 


17.88 


4140 


64.34 


16.06 


4670 


68.34 


16.71 


5200 


72.11 


17.32 


5730 


75.70 


17.89 


4150 


64.42 


16.07 


4680 


68.41 


16.73 


5210 


72.18 


17.34 


S740 


75.76 


17.90 


4160 


64.50 


16.08 


4690 


68.48 


16.74 


5220 


72.25 


17.35 


S750 


75.83 


17.92 


4170 


64.58 


16.10 


4700 


68.56 


16.75 


5230 


72.32 


17.36 


5760 


75.89 


17.93 


4180 


64.65 


16. II 


4710 


68.63 


16.76 


5240 


72.39 


17.37 


S770 


75.96 


17.94 


4190 


64.73 


16.12 


4720 


68.70 


16.77 


5250 


72.46 


17.38 


5780 


76.03 


17.95 


4200 


64.81 


16.13 


4730 


68.77 


16.79 


5260 


72.53 


17.39 


S790 


76.09 


17.96 


4210 


64.88 


16. IS 


4740 


68.85 


16.80 


5270 


72.59 


17.40 


5800 


76.16 


17.97 


4220 


64.96 


16.16 


4750 


68.92 


16.81 


5280 


72.66 


17.41 


5810 


76.22 


17.98 


4230 


65.04 


16.17 


4760 


68.99 


16.82 


5290 


72.73 


17.42 


5820 


76.29 


17.99 


4240 


65.12 


16.19 


4770 


69.07 


16.83 


5300 


72.80 


17-44 


5830 


76.35 


18 


4250 


65.19 


16.20 


4780 


69.14 


16.8s 


5310 


72.87 


17.4s 


5840 


76.42 


18.01 


4260 


65.27 


16.21 


4790 


69.21 


16.86 


S320 


72.94 


17.46 


5850 


76.49 


18.02 


4270 


65.35 


16.22 


4800 


69.28 


16.87 


S330 


73.01 


17.47 


5860 


76.55 


18.03 


4280 


65.42 


16.24 


4810 


69.35 


16.88 


S340 


73.08 


17.48 


5870 


76.62 


18.04 


4290 


65.50 


16.25 


4820 


69.43 


16.89 


5350 


73.14 


17.49 


5880 


76.68 


18.05 


4300 


65.57 


16.26 


4830 


69.50 


16.90 


5360" 


73.21 


17.50 


5890 


76.75 


18.06 


4310 


65. 65 


16.27 


4840 


69.57 


16.92 


5370 


73.28 


17.51 


5900 


76.81 


18.07 


4320 


65.73 


16.29 


4850 


69.64 


"16.93 


5380 


73.35 


17.52 


5910 


76.88 


18.08 



6o 



Mathematical Tables 



Table of Square Roots and Cube Roots of Numbers from 

looo to 10,000 — (Continued) 



No. 


Sq. 


Cube 


No. 


Sq. 


Cube 


No. 


Sq. 


Cube 


No. 


Sq. 


Cube 


root 


root 


root 


root 


root 


root 


root 


root 


5920 


76.94 


18.09 


6450 


80.31 


18.61 


6980 


83.55 


19. II 


7510 


86.66 


19 58 


S930 


77.01 


18.10 


6460 


80.37 


18.62 


6990 


83.61 


19 


.12 


7520 


86 


.72 


19.59 


5940 


77.07 


18. II 


6470 


80.44 


18.63 


7000 


83.67 


19 


.13 


7530 


86 


78 


19.60 


5950 


77.14 


18.12 


6480 


80.50 


18.64 


7010 


83.73 


19 


14 


7540 


86 


-83 


19.61 


5960 


77.20 


18.13 


6490 


80.56 


18.65 


7020 


83-79 


19 


IS 


7550 


86 


-89 


19.62 


5970 


77.27 


18.14 


6500 


80.62 


18.66 


7030 


83 -8s 


19 


.16 


7560 


86 


95 


19.63 


5980 


77.33 


18.15 


6510 


80.68 


18.67 


7040 


83-90 


19 


.17 


7570 


87 


.01 


19.64 


5990 


77.40 


18.16 


6520 


80.75 


18.68 


7050 


83-96 


19 


.17 


7580 


87 


06 


19.64 


6000 


77.46 


18.17 


6530 


80.81 


18.69 


7060 


84.02 


19 


.18 


7590 


87 


12 


19.65 


6010 


77.52 


18.18 


6540 


80.87 


18.70 


7070 


84.08 


19 


.19 


7600 


87 


18 


19.66 


6020 


77.59 


18.19 


6550 


80.93 


18.71 


7080 


84.14 


19 


20 


7610 


87 


24 


19.67 


6030 


77.65 


18.20 


6560 


80.99 


18.72 


7090 


84.20 


19 


.21 


7620 


87 


29 


19.68 


6040 


77.72 


18.21 


6570 


81.06 


18.73 


7100 


84.26 


19 


22 


7630 


87 


35 


19.69 


6050 


77.78 


18.22 


6580 


81.12 


18.74 


7110 


84.32 


19 


23 


7640 


87 


41 


19.70 


6060 


77.85 


18.23 


6590 


81.18 


18-75 


7120 


84.38 


19 


24 


7650 


87 


46 


19-70 


6070 


77.91 


18.24 


6600 


81.24 


18.76 


7130 


84.44 


19 


25 


7660 


87 


52 


19-71 


6080 


77.97 


18.2s 


6610 


81.30 


18.77 


7140 


84-50 


19 


26 


7670 


87 


58 


19-72 


6090 


78.04 


18.26 


6620 


81.36 


18.78 


7150 


84-56 


19 


26 


7680 


S7 


.64 


19-73 


6100 


78.10 


18.27 


6630 


81.42 


18.79 


7160 


84.62 


19 


27 


7690 


87 


69 


19-74 


6110 


78.17 


18.28 


6640 


81.49 


18.80 


7170 


84.68 


19 


28 


7700 


87 


75 


19-75 


6120 


78.23 


18.29 


6650 


81.55 


18.81 


7180 


84.73 


19 


29 


7710 


87 


81 


19-76 


6130 


78.29 


18.30 


6660 


81.61 


18.81 


7190 


84.79 


19 


30 


7720 


87 


86 


19.76 


6140 


78.36 


18.31 


6670 


81.67 


18.82 


7200 


84-85 


19 


31 


7730 


87 


92 


19.77 


6150 


78.42 


18.32 


6680 


81.73 


18.83 


7210 


84.91 


19 


32 


7740 


87 


98 


19 78 


6160 


78.49 


18.33 


6690 


81.79 


18.84 


7220 


84.97 


19 


33 


7750 


88 


03 


19.79 


6170 


78.55 


18.34 


6700 


81.85 


18.85 


7230 


85.03 


19 


34 


7760 


88 


09 


19.80 


6180 


78.61 


18.35 


6710 


81.91 


18.86 


7240 


85.09 


19 


35 


7770 


88 


15 


19.81 


6190 


78.68 


18.36 


6720 


81.98 


18.87 


7250 


85.15 


19 


35 


7780 


88 


20 


19.81 


6200 


78.74 


18.37 


6730 


82.04 


18.88 


7260 


85.21 


19 


36 


7790 


88 


26 


19.82 


6210 


78.80 


18.38 


6740 


82.10 


18.89 


7270 


85.26 


19 


37 


7800 


88 


32 


19.83 


6220 


78.87 


18.39 


6750 


82.16 


18.90 


7280 


85.32 


19 


38 


7810 


88 


37 


19.84 


6230 


78.93 


18.40 


6760 


82.22 


18.91 


7290 


85.38 


19 


39 


7820 


88 


43 


19-85 


6240 


78.99 


18.41 


6770 


82.28 


18.92 


7300 


85.44 


19 


40 


7830 


88 


49 


19.86 


6250 


79.06 


18.42 


6780 


82.34 


18.93 


7310 


85.50 


19 


41 


7840 


88 


54 


19.87 


6260 


79-12 


18.43 


6790 


82.40 


18.94 


7320 


85.56 


19 


42 


7850 


88 


60 


19-87 


6270 


79-18 


18.44 


6800 


82.46 


18.95 


7330 


85.62 


19 


43 


7860 


88 


66 


19.88 


6280 


79.25 


18.45 


6810 


82.52 


18.95 


7340 


85.67 


19 


43 


7870 


88 


71 


19.89 


6290 


79.31 


18.46 


6820 


82.58 


18.96 


7350 


85.73 


19 


44 


7880 


88 


77 


19.90 


6300 


79.37 


18.47 


6830 


82.64 


18.97 


7360 


85.79 


19 


45 


7890 


88 


83 


19.91 


6310 


79.44 


18.48 


6840 


82.70 


18.98 


7370 


85.85 


19 


46 


7900 


88 


88 


19.92 


6320 


79.50 


18.49 


6850 


82.76 


18.99 


7380 


85.91 


19 


47 


7910 


88 


94 


19.92 


6330 


79-56 


18.50 


6860 


82.83 


19 


7390 


85.97 


19 


48 


7920 


88 


99 


19.93 


6340 


79-62 


18.51 


6870 


82.89 


19.01 


7400 


86.02 


19 


49 


7930 


89 


05 


19.94 


6350 


79.69 


18.52 


6880 


82.95 


19.02 


7410 


86.08 


19 


50 


7940 


89 


II 


19.95 


6360 


79.75 


18.53 


6890 


83-01 


19-03 


7420 


86.14 


19 


50 


7950 


89 


16 


19.96 


6370 


79.81 


18.54 


6900 


83-07 


19-04 


7430 


86.20 


19 


51 


7960 


89 


22 


19.97 


6380 


79.87 


18.55 


6910 


83-13 


19 -05 


7440 


86.29 


19 


52 


7970 


89 


27 


19.97 


6390 


79.94 


18.56 


6920 


83.19 


19.06 


7450 


86.31 


19 


53 


7980 


89 


33 


19.98 


6400 


80 


18.57 


6930 


83.25 


19.07 


7460 


86.37 


19 


54 


7990 


89 


39 


19-99 


6410 


80.06 


18.58 


6940 


83.31 


19-07 


7470 


86.43 


19 


55 


8000 


89 


44 


20 


6420 


80.12 


18.59 


6950 


83.37 


19.08 


7480 


86.49 


19 


56 


8010 


89 


50 


20 01 


6430 


80.19 


18.60 


6960 


83.43 


19.09 


7490 


86.54 


19. 


57 


8020 


89 


55 


20.02 


6440 


80.25 


18.60 


6970 83.49 


19.10 


7500 


86.60 19. 


57 


8030 


89 


61 


20.02 



Table of Square Roots and Cube Roots 



6i 



Table of Square Roots and Cube Roots of Numbers from 
looo to 10,000 — {Contlmied) 



No. 


s,. 


Cube 


No. 


Sq. 


Cube 


No. 


Sq. 


Cube 


No. 


Sq. 


Cube 


root 


root 


root 


root 


root 


root 


root 


root 


8040 


89.67 


20.03 


8540 


92.41 


20.44 


9040 


95.08 


20.83 


9540 


97.67 


21.21 


8050 


89.72 


20.04 


8550 


92 


47 


20.45 


9050 


95 


14 


20.84 


9550 


97 


72 


21.22 


8060 


89.78 


20.05 


8560 


92 


52 


20.46 


9060 


95 


18 


20.85 


9560 


97 


78 


21.22 


8070 


89.83 


20.06 


8570 


92 


57 


20.46 


9070 


95 


24 


20.85 


9570 


97 


83 


21.23 


8080 


89.89 


20.07 


8580 


92 


63 


20.47 


9080 


95 


29 


20.86 


9580 


97 


88 


21.24 


8090 


89.94 


20.07 


8590 


92 


68 


20.48 


9090 


95 


34 


20.87 


9590 


97 


93 


21.25 


8100 


90 


20.08 


8600 


92 


74 


20.49 


9100 


95 


39 


20.88 


9600 


97 


98 


21.25 


8110 


90.06 


20.09 


8610 


92 


79 


20.50 


91 10 


95 


45 


20.89 


9610 


98 


03 


21.26 


8120 


90.11 


20.10 


8620 


92 


84 


20.50 


9120 


95 


50 


20.89 


9620 


98 


08 


21.27 


8130 


90.17 


20.11 


8630 


92 


90 


20.51 


9130 


95 


55 


20.90 


9630 


98 


13 


21.28 


8140 


90.22 


20.12 


8640 


92 


95 


20.52 


9140 


95 


60 


20.91 


9640 


98 


18 


21.28 


8150 


90.28 


20.12 


8650 


93 


01 


20. S3 


9150 


95 


66 


20.92 


9650 


98 


23 


21.29 


8160 


90.33 


20.13 


8660 


93 


06 


20.54 


9160 


95 


71 


20.92 


9660 


98 


29 


21.30 


8170 


90.39 


20.14 


8670 


93 


II 


20.54 


9170 


95 


76 


20.93 


9670 


98 


34 


21.30 


8180 


90.44 


20.15 


8680 


93 


17 


20.55 


9180 


95 


81 


20.94 


9680 


98 


39 


21.31 


8190 


90.50 


20.16 


8690 


93 


22 


20.56 


9190 


95 


86 


20.95 


9690 


98 


44 


21.32 


8200 


90.55 


20.17 


8700 


93 


27 


20.57 


9200 


95 


92 


20.9s 


9700 


98 


49 


21.33 


8210 


90.61 


20.17 


8710 


93 


33 


20.57 


9210 


95 


97 


20.96 


9710 


98 


54 


21.33 


8220 


90.66 


20.18 


8720 


93 


38 


20.58 


9220 


96 


02 


20.97 


9720 


98 


59 


21.34 


8230 


90.72 


20.19 


8730 


93 


43 


20.59 


9230 


96 


07 


20.98 


9730 


98 


64 


21.35 


8240 


90.77 


20.20 


8740 


93 


49 


20.60 


9240 


96 


12 


20.98 


9740 


98 


69 


21.36 


8250 


90.83 


20.21 


8750 


93 


54 


20.61 


9250 


96 


18 


20.99 


9750 


98 


74 


21.36 


8260 


90.88 


20.21 


8760 


93 


59 


20.61 


9260 


96 


23 


21 


9760 


98 


79 


21.37 


8270 


90.94 


20.22 


8770 


93 


65 


20.62 


9270 


96 


28 


21.01 


9770 


98 


84 


21.38 


8280 


90.99 


20.23 


8780 


93 


70 


20.63 


9280 


96 


33 


21.01 


9780 


98 


89 


21.39 


8290 


91.05 


20.24 


8790 


93 


75 


20.64 


9290 


96 


38 


21.02 


9790 


98 


94 


21.39 


8300 


91.10 


20.25 


8800 


93 


81 


20.65 


9300 


96 


44 


21.03 


9800 


98 


99 


21.40 


8310 


91.16 


20.26 


8810 


93 


86 


20.65 


9310 


96 


49 


21.04 


9810 


99 


05 


21.41 


8320 


91.21 


20.26 


8S20 


93 


91 


20.66 


9320 


96 


54 


21.04 


9820 


99 


10 


21.41 


8330 


91.27 


20.27 


8830 


93 


97 


20.67 


9330 


96 


59 


21.05 


9830 


99 


15 


21.42 


8340 


91.32 


20.28 


8840 


94 


02 


20.68 


9340 


96 


64 


21.06 


9840 


99 


20 


21.43 


8350 


91.38 


20.29 


8850 


94 


07 


20.68 


9350 


96 


70 


21.07 


9850 


99 


25 


21.44 


8360 


91.43 


20.30 


8860 


94 


13 


20.69 


9360 


96 


75 


21.07 


9860 


99 


30 


21.44 


8370 


91.49 


20.30 


8870 


94 


18 


20.70 


9370 


96 


80 


21.08 


9870 


99 


35 


21.45 


8380 


91.54 


20.31 


8880 


94 


23 


20.71 


9380 


96 


85 


21.09 


9880 


99 


40 


21.46 


8390 


91.60 


20.32 


8890 


94 


29 


20.72 


9390 


96 


90 


21.10 


9890 


99 


45 


21.47 


8400 


91.65 


20.33 


8900 


94 


34 


20.72 


9400 


96 


95 


21.10 


9900 


99 


50 


21.47 


8410 


91.71 


20.34 


8910 


94 


39 


20.73 


9410 


97 


01 


21. II 


9910 


99 


55 


21.48 


8420 


91.76 


20.34 


8920 


94 


45 


20.74 


9420 


97 


06 


21.12 


9920 


99 


60 


21.49 


8430 


91.82 


20.35 


8930 


94 


50 


20.7s 


9430 


97 


II 


21.13 


9930 


99 


65 


21.49 


8440 


91.87 


20.36 


8940 


94 


55 


20.75 


9440 


97 


16 


21.13 


9940 


99 


70 


21.50 


8450 


91.92 


20.37 


8950 


94 


60 


20.76 


9450 


97 


21 


21.14 


9950 


99 


75 


21.51 


8460 


91.98 


20.38 


8960 


94 


66 


20.77 


9460 


97 


26 


21.15 


9960 


99 


80 


21.52 


8470 


92.03 


20.38 


8970 


94 


71 


20.78 


9470 


97 


31 


21.16 


9970 


99 


85 


21.52 


8480 


92.09 


20.39 


8980 


94 


76 


20.79 


9480 


97 


37 


21.16 


9980 


99 


90 


21.53 


8490 


92.14 


20.40 


8990 


94 


82 


20.79 


9490 


97 


42 


21.17 


9990 


99 


95 


21.54 


85cx> 


92.20 


20.41 


9000 


94 


87 


20.80 


9500 


97 


47 


21.18 


lOOOO 


100 


21.54 


8510 


92.25 


20.42 


9010 


94 


92 


20.81 


9510 


97 


.52 


21.19 








8520 


92.30 


20.42 


9020 


94 


97 


20.82 


9520 


97 


.57 


21.19 








8530 


92.36 


20.43 


9030 


95 


03 


20.82 


9S30 


97 


62 


21.20 









62 Mathematical Tables 

To find Square or Cube Roots of large numbers not con- 
tained in the column of numbers of the table 

Such roots may sometimes be taken at once from the table, by merely 
regarding the columns of powers as being columns of numbers; and those 
of numbers as being those of roots. Thus, if the square root of 25281 
is required, first find that number in the column of squares; and opposite 
to it, in the column of numbers, is its square root 159. For the cube root 
of 857375, find that number in the column of cubes; and opposite to it, 
in the colimin of numbers, is its cube root 95. When the exact number 
is not contained in the column of squares, or cubes, as the case may be, 
we may use instead the number nearest to it, if no great accuracy is 
required. But when a considerable degree of accuracy is necessary, the 
following very correct methods may be used. 

For the square root 

This rule appHes both to whole numbers and to those which are partly 
(not wholly) decimal. First, in the foregoing manner, take out the 
tabular number, which is nearest to the given one; and also its tabular 
square root. Multiply this tabular number by 3; to the product add 
the given number. Call the sum A . Then multiply the given number 
by 3; to the product add the tabular number. Call the sum 5. Then 
A \ B :'. Tabular root : Required root. 

Example. — Let the given number be 946.53. Here we find the nearest 
tabular number to be 947; and its tabular square root 30.7734. Hence, 



947 = tabular number 
3 


■ and ■ 
59 " 


946.53 = given number 
3 


2841 
946.53 = given number 


2839-59 
947 = tabular number 


3787.53 - A. 

A B 

en 3787.53 : 3786 


,3786.59 = B. 

Tab. root Req'd root 

30.7734 : 30.7657+. 



The root as found by actual mathematical process is also 30.7657+. 

For the cube root 

This rule applies both to whole mmabers and to those which are parity 
decimal. First take out the tabular number which is nearest to the given 
one; and also its tabular cube root. Multiply this tabular nimiber by 
2; and to the product add the given number. Call the sum A. Then 



Cube Root 



63 



multiply the given number by 2; and to the product add the tabular 
number. Call the sum B. Then 

A : B :: Tabular root : Required root. 

Example. — Let the given number be 7368. Here we find the nearest 
tabular number (in the column of cubes) to be 6859; and its tabular cube 
root 19. Hence, 



6859 = tabular number 



13718 
7368 = given number 



21086 = A. 



and 



7368 = given number 

2 



14736 
6859 



tabular number 
B. 



2159s 
B Tab. root Req'd root 

Then 21086 : 21595 '■ ^9 * i9-4S85. 

The root as found by correct mathematical process is 19.4588 



A 

21086 



64 



Mathematical Tables 



Areas and Circumferences of Circles for Diameters m 
Units and Eighths, etc., from Yg^ to ioo. 



Diatn- 


Circum- 


Area 


Diam- 


Circum- 


Area 


Diam- 


Circum- 


Area 


eter 


ference 


eter 


ference 


eter 


ference 


1/64 


.049087 


.00019 


21/ 


7.06858 


3.9761 


5Me 


17.4751 


24.301 


H2 


.098175 


.00077 


■Me 


7.26493 


4.2000 


H 


17.6715 


24.850 


3/64 


.147262 


.00173 


% 


7.46128 


4.4301 


IMe 


17.8678 


25.406 


Me 


.196350 


.00307 


Me 


7.65763 


4.6664 


M 


18.0642 


25.967 


H2 


.294524 


.00690 


1/2 


7.85398 


4.9087 


IMe 


18.2605 


26.535 


H 


.392699 


.01227 


Me 


8.05033 


5.1572 


Ms 


18.4569 


27.109 


%2 


.490874 


.01917 


Ms 


8.24668 


5.4119 


IMe 


18.6532 


27.688 


3/6 


.589049 


.02761 


ii/e 


8.44303 


5.6727 


6 


18.8496 


28.274 


1^2 


.687223 


.03758 


M 


8.63938 


5.9396 


\i 


19.2423 


29.465 


H 


.785398 


.04909 


iMe 


8.83573 


6.2126 


M 


19.6350 


30.680 


%2 


.883573 


.06213 


Ms 


9.03208 


6.4918 


H 


20.0277 


31.919 


Mo 


.981748 


.07670 


iMe 


9.22843 


6.7771 


i/i 


20.4204 


33.183 


IH2 


1.07992 


.09281 


3 


9.42478 


7.0686 


n 


20.8131 


34.472 


% 


I . 17810 


. II04S 


Me 


9.62113 


7.3662 


M 


21.2058 


35.785 


^H2 


1.27627 


. 12962 


i/i 


9.81748 


7.6699 


% 


21.5984 


37.122 


7/6 


1.37445 


. 15033 


Me 


10.0138 


7.9798 


7 


21. 991 I 


38.485 


15^2 


1.47262 


.17257 


1/ 


10.2102 


8.2958 


i/i 


22.3838 


39.871 


1/ 


1.57080 


.19635 


Me 


10.4065 


8.6179 


M 


22.7765 


41.282 


lj^2 


1.66897 


.22166 


% 


10.6029 


8.9462 


% 


23.1692 


42.718 


ri6 


I . 76715 


.24850 


Me 


10.7992 


9.2806 


M 


23.5619 


44.179 


1%2 


1.86532 


.27688 


1/2 


10.9956 


9.6211 


H 


23.9546 


45.664 


5/i 


1.96350 


.30680 


Me 


11.1919 


9.9678 


3/4 


24.3473 


47.173 


2^2 


2.06167 


.33824 


5.^ 


11.3883 


10.321 


Ms 


24.7400 


48.707 


11/6 


2.15984 


.37122 


i/e 


11.S846 


10.680 


8 


25.1327 


50.265 


^%2 


2.25802 


.40574 


M 


I I. 7810 


11.045 


i/i 


25.5254 


51.849 


% 


2.35619 


.44179 


iMe 


11.9773 


II. 416 


M 


25.9181 


53.456 


2^2 


2.45437 


.47937 


% 


12.1737 


11.793 


H 


26.3108 


55.088 


13/6 


2.55254 


.51849 


IMe 


12.3700 


12.177 


H 


26.703s 


56.745 


27/^2 


2 . 65072 


■55914 


4 


12.5664 


12.566 


H 


27.0962 


58.426 


% 


2.74889 


.60132 


He 


12.7627 


12.962 


H 


27.4889 


60.132 


2%2 


2.84707 


.64504 


i/i 


12.9591 


13.364 


% 


27.8816 


61.862 


1-/6 


2.94524 


.69029 


Me 


13.1554 


13.772 


9 


28.2743 


63.617 


3^2 


3.04342 


.73708 


1/ 


13.3518 


14.186 


i/i 


28.6670 


65.397 


I 


3.14159 


.78540 


Me 


13.5481 


14.607 


M 


29.0597 


67.201 


1/6 


3.33794 


.88664 


H 


13.7445 


15.033 


H 


29.4524 


69.029 


'A 


3.53429 


.99402 


Me 


13.9408 


15.466 


H 


29.8451 


70.882 


?i6 


3.73064 


I . 1075 


1/ 


14.1372 


15.904 


H 


30.2378 


72.760 


M 


3.92699 


I . 2272 


Me 


14.3335 


16.349 


% 


30.6305 


74.662 


5/6 


4.12334 


1.3530 


Ms 


14.5299 


16.800 


% 


31.0232 


76.589 


% 


4.31969 


1.4849 


i/e 


14.7262 


17.257 


IC 


31.4159 


78.540 


Vi6 


4.51604 


1.6230 


% 


14.9226 


17.721 


H 


31.8086 


80.516 


¥i 


4.71239 


I. 7671 


IMe 


15.1189 


18.190 


M 


32.2013 


82.516 


9/6 


4.90874 


I. 9175 


% 


15.3153 


18.665 


% 


32.5940 


84.541 


H 


5.10509 


2.0739 


IMe 


15.5116. 


19.147 


1/ 


32.9867 


86.590 


1/6 


5.30144 


2.2365 


5 


15.7080 


19.635 


5.^ 


33-3794 


88.664 


3/ 


5. 49779 


2.4053 


Me 


15.9043 


20.129 


3/4 


33.7721 


90.763 


13/6 


5.69414 


2.5802 


% 


16.1007 


20.629 . 


i^i 


34.1648 


92.886 


% 


5.89049 


2.7612 


Me 


16.2970 


21.135 


II 


34.5575 


95.033 


15/6 


6.08684 


2.9483 


M 


16.4934 


21.648 


H 


34.9502 


97.205 


2 


6.28319 


3.1416 


Me 


16.6897 


22.166 


H 


35.3429 


99.402 


1/6 


6.47953 


3.3410 


H 


16.8861 


22.691 


% 


35.7356 


101.62 


^ 


6.67588 


3.5466 


Me 


17.0824 


23.221 


1/2 


36.1283 


103.87 


Me 


6.87223 


3.7583 


M2 


17.2788 


23.758 


5/i 


36.5210 


106.14 



Areas and Circumferences of Circles 



65 



Areas and Circumterences of Circles for Diameters in 
Units and Eighths, etc. — (Continued) 



Diam- 


Circum- 


Area 


Diam- 


Circum- 


Area 


Diam- 


Circum- 


Area 


eter 


ference 


eter 


ference 


eter 


ference 


im 


36.9137 


108.43 


im 


57-7268 


265-18 


25 


78.5398 


490.87 


■"yi 


37.3064 


110.75 


Vi 


58.1195 


268.80 


% 


78.9325 


495.79 


12 


37.6991 


113. 10 


% 


58.5122 


272.45 


V 


79-3252 


500.74 


H 


38.0918 


IIS. 47 


% 


58.9049 


276.12 


H 


79-7179 


505.71 


Vi 


38.4845 


117.86 


^A 


59.2976 


279.81 


V2 


80.1106 


S10.71 


H 


38.8772 


120.28 


19 


59.6903 


283.53 


Vs 


80.5033 


515.72 


H 


39.2699 


122.72 


A 


60.0830 


287.27 


¥i 


80.8960 


520.77 


% 


39.6626 


125.19 


M 


60.4757 


291.04 


Vs 


81.2887 


525.84 


¥i 


40.0553 


127.68 


rs 


60.8684 


294.83 


26 


81.6814 


530.93 


% 


40.4480 


,130.19 


V2 


61.2611 


298.65 


M 


82.0741 


536.0s 


13 


40.8407 


132.73 


Y?, 


61.6538 


302.49 


Vi 


82.4668 


541 • 19 


\i 


41.2334 


135.30 


¥i 


62.0465 


306.3s 


3/8 


82.8595 


546.35 


H 


41.6261 


137.89 


'A 


62.4392 


310.24 


V2 


83.2522 


551-55 


3/8 


42.0188 


140.50 


20 


62.8319 


314.16 


5/8 


83.6449 


556.76 


H 


42.411S 


143.14 


A 


63 . 2246 


318.10 


% 


84.0376 


562.00 


% 


42.8042 


145-80 


Vi 


63-6173 


322.06 


% 


84.4303 


567.27 


% 


43.1969 


148.49 


H 


64.0100 


326.05 


27 


84.8230 


572.56 


% 


43.S896 


151.20 


y2 


64.4026 


330.06 


A 


85-2157 


577.87 


14 


43.9823 


153-94 


5/8 


64.7953 


334.10 


Vi 


85.6084 


583-21 


i/i 


44.3750 


156-70 


% 


65.1880 


338.16 


y& 


86.0011 


588.57 


\i 


44.7677 


159-48 


A 


65.5807 


342.25 


V2 


86.3938 


593.96 


% 


45.1604 


162.30 


21 


65.9734 


346.36 


n 


86.786s 


599.37 


¥2 


45.5531 


165.13 


Vs' 


66.3661 


350.50 


Vi 


87.1792 


604.81 


5,i 


45.9458 


167.99 


H 


66.7588 


354.66 


A 


87.5719 


610.27 


% 


46.3385 


170.87 


% 


67.1515 


358.84 


28 


87.9646 


615.7s 


% 


46.7312 


173.78 


¥2 


67.5442 


363.05 


H 


88.3573 


621.26 


IS 


47-1239 


176.71 


5/g 


67.9369 


367-28 


Vi 


88.7500 


626.80 


H 


47.5166 


179.67 


% 


68.3296 


371-54 


% 


89.1427 


632.36 


Vi 


47.9093 


182.65 


Vs 


68.7223 


375-83 


V2 


89.5354 


637 -94 


% 


48.3020 


185.66 


22 


69.1150 


380.13 


^A 


89.9281 


643-55 


Vi 


48.6947 


188.69 


Vs 


69.5077 


384.46 


Vi 


90.3208 


649-18 


H 


49.0874 


191-75 


H 


69.9004 


388.82 


% 


90.7135 


654.84 


% 


49-4801 


194-83 


% 


70.2931 


393-20 


29 


91 . 1062 


660.52 


'A 


49.8728 


197-93 


V2 


70.6858 


397-61 


A 


91.4989 


666.23 


16 


50.2655 


201.06 


% 


71.0785 


402.04 


Vi 


91.8916 


671-96 


H 


SO. 6582 


204.22 


% 


71.4712 


406.49 


% 


92.2843 


677.71 


Vi 


51-0509 


207.39 


A 


71.8639 


410.97 


V2 


92.6770 


683.49 


% 


SI -4436 


210.60 


23 


72.2566 


415.48 


% 


93.0697 


689.30 


Vi 


SI -8363 


213.82 


M 


72.6493 


420.00 


% 


93.4624 


695.13 


% 


52.2290 


217.08 


H 


73.0420 


424.56 


li 


93.8551 


700.98 


% 


52.6217 


220.35 


y& 


73.4347 


429.13 


30 


94-2478 


706.86 


% 


53.0144 


223.65 


V2 


73-8274 


433-74 


A 


94-6405 


712.76 


17 


53.4071 


226.98 


^ 


74 -2201 


438-36 


Vi 


95.0332 


718.69 


\i 


53.7998 


230.33 


% 


74-6128 


443-01 


H 


95.4259 


724.64 


H 


54.1925 


233.71 


li 


75.0055 


447-69 


V2 


95.8186 


730.62 


H 


54.5852 


237.10 


24 


75-3982 


452-39 


5/8 


96.2113 


736.62 


Vi 


54.9779 


240.53 


H 


75-7909 


457-11 


¥i 


96.6040 


742.64 


% 


55-3706 


243.98 


Vi 


76.1836 


461.86 


li 


96.9967 


748.69 


% 


55.7633 


247.45 


n 


76.5763 


466.64 


31 


97.3894 


754-77 


% 


56 . 1560 


250.95 


V2 


76.9690 


471.44 


A 


97.7821 


760.87 


18 


56.5487 


254-47 


Vs 


77.3617 


476.26 


Vi 


98.1748 


766.99 


H 


56.9414 


258.02 


% 


77-7544 


481. II 


% 


98.5675 


773-14 


H 


57.3341 


261.59 


% 


78.1471 


485.98 


V2 


98.9602 


779-31 



66 



Mathematical Tables 



Areas and Circumferences of Circles for Diameters in 
Units and Eighths, etc. — {Continued) 



Diam- 


Circum- 


Area 


Diam- 


Circum- 


Area 


Diam- 


Circum- 


Area 


eter 


ference 


eter 


ference 


eter 


ference 


3l5^ 


99-3529 


785-51 


H 


120,166 


1149.1 


AA% 


140.979 


1581.6 


% 


99-7456 


791.73 


H 


120.559 


1156.6 


45 


141.372 


1590.4 


% 


100.138 


797.98 


V2 


120.951 


1164.2 


A 


141 . 764 


1599.3 


32 


100.531 


804.25 


H 


121.344 


1171.7 


Vi 


142.157 


1608.2 


H 


100.924 


810,54 


¥i 


121.737 


1179.3 


% 


142.550 


1617.0 


W • 


loi . 316 


816.86 


li 


122.129 


1186.9 


\^ 


142 . 942 


1626.0 


% 


loi . 709 


823 . 21 


39 


122.522 


1194.6 


% 


143.335 


1634.9 


y2 


102.102 


829.58 


1/8 


122.915 


1202.3 


% 


143.728 


1643.9 


% 


102.494 


835.97 


Vi 


123.308 


1210.0 


A 


144. 121 


1652.9 


% 


102.887 


842.39 


% 


123,700 


1217.7 


46 


144.513 


1661.9 


% 


103.280 


848.83 


. ¥2 


124.093 


1225.4 


A 


144.906 


1670.9 


33 


103.673 


855.30 


% 


124.486 


1233.2 


M 


145.299 


1680.0 


% 


104.065 


861.79 


% 


124.878 


1241.0 


% 


145.691 


1689. I 


H 


104.458 


868.31 


Vs 


125.271 


1248.8 


A 


146.084 


1698.2 


% 


104.851 


874.85 


40 


125.664 


1256.6 


A 


146.477 


1707.4 


H 


105.243 


881.41 


Vs 


126.056 


1264.5 


% 


146.869 


1716.5 


^A 


105.636 


888.00 


14 


126.449 


1272.4 


A 


147.262 


1725.7 


% 


106.029 


894.62 


H 


126,842 


1280.3 


47 


147.655 


1734.9 


% 


106.421 


901.26 


Vi 


127.235 


1288. 2 


A 


148.048 


1744.2 


34 


106.814 


907.92 


% 


127.627 


1296.2 


A 


148 . 4JO 


1753. 5 


H 


107.207 


914.61 


%. 


128.020 


1304.2 


H 


148.833 


1762.7 


H 


107.600 


921.32 


% 


128.413 


1312.2 


A 


149.226 


1772. I 


% 


107.992 


928.06 


41 


128.805 


1320.3 


A 


149.618 


1781.4 


H 


108.385 


934.82 


M 


129.198 


1328.3 


% 


150. 01 I 


1790.8 


% 


108.778 


941.61 


H 


129.591 


1336.4 


A 


150.404 


1800. I 


% 


109.170 


948.42 


% 


129.983 


1344.5 


48 


150.796 


1809.6 


% 


109.563 


955.25 


Vi 


130.376 


1352.7 


Vs 


151 . 189 


1819.0 


35 


109.956 


962.11 


5/8 


130.769 


1360.8 


A 


151 582 


1828.5 


H 


110.348 


969.00 


M 


131. 161 


1369 


A 


151.975 


1837.9 


H 


no. 741 


975.91 


''A 


131.554 


1377-2 


V2 


152.367 


1847.5 


% 


III. 134 


982.84 


42 


131.947 


1385.4 


A 


152.760 


1857.0 


^ 


III. 527 


989.80 


A 


132.340 


1393.7 


% 


153.153 


1866.5 


5i 


III. 919 


996.78 


H 


132.732 


1402.0 


A 


153.545 


1876. I 


% 


112. 312 


1003.8 


Vs 


133.125 


1410.3 


49 


153.938 


1885.7 


^ 


112.705 


1010.8 


H 


133-518 


1418.6 


A 


154.331 


1895.4 


36 


113-097 


1017.9 


H 


133-910 


1427.0 


Vi 


154.723 


1905.0 


H 


113.490 


1025 . 


% 


134-303 


1435.4 


A 


155. 116 


1914.7 


M 


113.883 


1032 . I 


li 


134.696 


1443.8 


A 


155.509 


1924.4 


% 


114.275 


1039.2 


43 


135.088 


1452.2 


A 


155.902 


1934.2 


J^ 


114.668 


1046.3 


% 


135.481 


1460.7 


% 


156.294 


1943.9 


^ 


I 15. 061 


1053.5 


Yi 


135.874 


1469. I 


A 


156.687 


1953.7 


14 


115-454 


1060.7 


% 


136.267 


1477.6 


50 


157.080 


1963. 5 


% 


115.846 


1068.0 


V2 


136.659 


1486.2 


A 


157.472 


1973.3 


37 


116.239 


1075.2 


Vs 


137.052 


1494.7 


A 


157.865 


1983.2 


^ 


116.632 


1082.5 


V 


137.445 


1503.3 


A 


158.258 


1993. I 


M 


117.024 


1089,8 


Vs 


137.837 


1511.9 


I/, 


158.650 


2003.0 


^ 


II7-417 


1097. I 


44 


138 . 230 


1520.5 


A 


159.043 


2012.9 


J^ 


117. 810 


1104.5 


i/i 


138.623 


1529.2 


% 


159.436 


2022.8 


^ 


118.202 


nil. 8 


H 


139 015 


1537.9 


A 


159.829 


2032.8 


% 


118.596 


1119.2 


H 


139.408 


1546.6 


51 


160.221 


2042.8 


% 


118.988 


1126.7 


H 


139.801 


1555.3 


A 


160.614 


2052.8 


38 


119 -381 


1134.1 


^A 


140.194- 


1564.0 


H 


161.007 


2062.9 


H 


119.773 


1141.6 


% 


140.586 


1572.8 


A 


161.399 


2073.0 



Areas and Circumferences of Circles 



67 



Areas and Circumferences of Circles for Diameters in 
Units and Eighths, etc. — {Continued) 



Diam- 


Circum- 


Area 


Diam- 


Circum- 


Area 


Diam- 


Circum- 




eter 


ference 


eter 


ference 


eter 


ference 


Area 


51H 


161.792 


2083.1 


5814 


182.605 


2653.5 


64^/4 


203 , 418 


3292.8 


% 


162.185 


2093.2 


H 


182.998 


2664.9 


l^ 


203 811 


3305-6 


% 


162.577 


2103.3 


% 


183.390 


2676.4 


65 


204.204 


3318.3 


% 


162.970 


2II3-5 


H 


183.783 


2687.8 


\^ 


204-596 


3331 -I 


52 


163.363 


2123.7 


H 


184.176 


2699.3 


Yi 


204.989 


3343.9 


% 


163.756 


2133-9 


% 


184.569 


2710.9 


% 


205.382 


3356.7 


H 


164.148 


2144.2 


% 


184.961 


2722.4 


\^ 


205.774 


3369.6 


% 


164.541 


2154.5 


59 


185-354 


2734.0 


% 


206.167 


3382.4 


H 


164.934 


2164.8 


i/i 


185.747 


2745.6 


¥i 


206.560 


3395.3 


H 


165.326 


2175. I 


H 


186.139 


2757.2 


% 


206.952 


3408.2 


% 


165-719 


2185.4 


% 


186.532 


2768.8 


66 


207.345 


3421.2 


li 


166. 112 


2195-8 


Vi 


186.925 


2780.5 


\i 


207.738 


3434.2 


53 


166.504 


2206.2 


% 


187-317 


2792.2 


Yi 


208.131 


3447.2 


H 


166.897 


2216.6 


% 


187-710 


2803.9 


% 


208.523 


3460.2 


H 


167.290 


2227.0 


% 


188.103 


2815.7 


Yz 


208.916 


3473.2 


% 


167.683 


2237.5 


60 


188.496 


2827-4 


% 


209.309 


3486.3 


\^ 


168.075 


2248.0 


H 


188.888 


. 2839.2 


% 


209.701 


3499.4 


% 


168.468 


2258.5 


Yi 


189.281 


2851.0 


'A 


210.094 


3512.5 


% 


168.861 


2269.1 


H 


189.674 


. 2862.9 


67 


210.487 


3525.7 


% 


169.253 


2279.6 


1/2 


190.066 


2874. 8 


H 


210.879 


3538.8 


54 


169.646 


2290.2 


5/8 


190.459 


2886.6 


Yi 


211.272 


3552.0 


li 


170.039 


2300.8 


% ■ 


190.852 


2898.6 


H 


211.665 


3565.2 


3/4 


170.431 


2311.5 


li 


191.244 


2910.5 


1/2 


212.058 


3578.5 


% 


170.824 


2322.1 


61 


191.637 


2922.5 


H 


212.450 


3591.7 


H 


171. 217 


2332.8 


Yi 


192.030 


2934.5 


% 


212.843 


3605.0 


n 


171.609 


2343-5 


Yi 


192.423 


2946.5 


'A 


213.236 


3618.3 


% 


172.002 


2354-3 


% 


192.815 


2958.5 


68 


213.628 


3631.7 


li 


172.39s 


2365.0 


' Y2 


193-208 


2970.6 


% 


214.021 


3645.0 


55 


172.788 


2375-8 


H 


193.601 


2982.7 


Yi 


214.414 


3658.4 


H 


173.180 


2386.6 


% 


193.993 


2994.8 


% 


214.806 


3671.8 


H 


173.573 


2397.5 


% 


194.386 


3006.9 


Y2 


215.199 


3685.3 


% 


173.966- 


2408.3 


62 


194.779 


3019. I 


% 


215.592 


3698.7 


Vi 


174.358 


2419.2 


M 


195. 171 


3031.3 


Yi 


215.984 


3712.2 


H 


174.751 


2430.1 


Yi 


195.564 


3043.5 


'A 


216.377 


3725.7 


% 


175.144 


2441 . I 


Yb 


195.957 


3055.7 


■69 


216.770 


3739.3 


% ■ 


175.536 


2452 


Yi 


196.350 


3068.0 


A 


217.163 


3752.8 


56 


175.929 


2463.0 


5/8 


196.742 


3080.3 


Yi 


217.555 


3766.4 


M 


176.322 


2474.0 


/•4 


197.135 


3092.6 


H 


217.948 


3780.0 


H 


176.715 


2485.0 


l^ 


197.528 


3104.9 


A 


218.341 


3793.7 


H 


177.107 


2496.1 


63 


197.920 


3117.2 


% 


218.733 


3807.3 


H 


177.500 


2507.2 


\i 


198.313 


3129.6 


% 


219.126 


3821.0 


% 


177.893 


2518.3 


Yi 


198.706 


3142.0 


A 


219.519 


3834.7 


% 


178.285 


2529.4 


% 


199.098 


3154.5 


70 


219. 911 


3848.5 


% 


178.678 


2540.6 


Y. 


199.491 


3166.9 


A 


220.304 


3862.2 


57 


179 071 


2551.8 


rs 


199.884 


3179.4 


Yi 


220.697 


3876.0 


H 


179.463 


2563.0 


% 


200.277 


3191.9 


A 


221.090 


3889.8 


Yi 


179.856 


2574.2 


% 


200.669 


3204.4 


Y2 


221.482 


3903.6 


H 


180.249 


2585.4 


64 


201.062 


3217.0 


5/8 


221.875 


3917. 5 


H 


180.642 


2596.7 


M 


201.455 


3229.6 


Yi 


222 . 268 


3931.4 


H 


181.034 


2608.0 


Yi 


-201.847 


3242.2 


A 


222.660 


3945.3- 


H 


181.427 


2619.4 


% 


202.240 


3254.8 


71 


223.053 


3959-2 


% 


181.820 


2630.7 


H 


202.633 


3267.5 


A 


223.446 


3973.1 


58 


182.212 


2642.1 


% 


203.02s 


3280.1 


Yi 


223.838 


3987.1 



68 



Mathematical Tables 



Areas and Circumferences of Circles for Diameters in 
Units and Eighths, etc. — (Continued) 



Diam- 


Circum- 




Diam- 


Circum- 




Diam- 


Circum- 




eter 


ference 


Area 


eter 


ference 


Area 


eter 


ference 


Area 


im 


224.231 


4001. I 


78 


245.044 


4778.4 


84H 


265.857 


5624.5 


H 


224.624 


, 401S.2 


H 


245.437 


4793.7 


3/4 


266.250 


5641.2 


H 


225.017 


4029.2 


H 


245 830 


4809.0 


li 


266.643 


5657.8 


% 


225.409 


4043.3 


3/8 


246.222 


4824.4 


85 


267.035 


5674.5 


^ 


225 . 802 


4057.4 


1/2 


246.615 


4839 .8 


H 


267.428 


5691.2 


72 


226.195 


4071.5 


H 


247.008 


4855.2 


/4 


267.821 


5707.9 


H 


226.587 


4085.7 


3/4 


247.400 


4870.7 


% 


268.213 


5724.7 


M 


226.980 


4099.8 


li 


247.793 


4886.2 


1/-2 


268.606 


5741 -5 


H 


227.373 


41140 


79 


248.186 


4901.7 


^A 


268.999 


5758-3 


Vi 


227.765 


4128.2 


H 


248.579 


4917-2 


% 


269.392 


5775 -I 


^A 


228.158 


4142.5 


Vi 


248.971 


4932 .-7 


% 


269.784 


5791-9 


% 


228.551 


4156.8 ■ 


3/8 


249 364 


4948.3 


86 


270.177 


5808.8 


% 


228.944 


4171.1 


/2 


249-757 


4963.9 


M 


270.570 


5825.7 


73 


229.336 


4185.4 


% 


250.149 


4979-5 


H 


270.962 


5842.6 


^ 


229.729 


4199.7 


3/4 


250.542 


4995-2 


% 


271.355 


5859-6 


H 


230.122 


4214. I 


li 


250.935 


5010.9 


Vi 


271 . 748 


5876-5 


% 


230.514 


4228.5 


80 


251.327 


5026.5 


rs 


272.140 


5893-5 


Vz 


230.907 


4242.9 


% 


251.720 


5042.3 


3/4 


272.533 


5910 -6 


% 


231.300 


4257.4 


M 


252.113 


5058.0 


Ji 


272.926 


5927-6 


% 


231.692 


4271.8 


% 


252.506 


5073.8 


87 


273.319 


5944-7 


% 


232.085 


4286.3 


/2 


252.898 


5089.6 


\^ 


273.711 


5961.8 


74 


232.478 


4300.8 


54 


253.291 


5105.4 


Vi 


274.104 


5978.9 


\^ 


232.871 


4315.4 


% 


253.684 


5121.2 


% 


274.497 


5996.0 


% 


233.263 


4329.9 


. H 


254.076 


5137.1 


\^ 


274.889 


6013 . 2 


% 


233.656 


4344.5 


81 


254.469 


5153-0 


H 


275.282 


6030.4 


V2 


234.049 


4359.2 


H 


254.862 


5168.9 


% 


275-675 


6047.6 


% 


234.441 


4373.8 


H 


255 . 254 


5184.9 


% 


276.067 


6064.9 


% 


234.834 


4388.5 


% 


255.647 


5200.8 


88 


276.460 


6082.1 


■"A 


235.227 


4403.1 


1/2 


256.040 


5216.8 


A 


276.853 


6099.4 


75 


235.619 


4417.9 


% 


256.433 


5232.8 


H 


277.246 


6116.7 


H 


236.012 


4432.6 


% 


256.825 


5248.9 


% 


277.638 


6134- I 


H 


236.405 


4447.4 


li 


257.218 


5264.9 


H 


278.031 


6151.4 


3/8 


236.798 


4462.2 


82 


257.611 


5281.0 


H 


278.424 


6168.8 


1/2 


237.190 


4477.0 


M 


258.003 


5297-1 


34 


278.816 


6186.2 


% 


237.583 


4491-8 


M 


258.396 


5313-3 


'A 


279.209 


6203.7 


% 


237.976 


4506.7 


3/8 


258.789 


5329-4 


89 


279 . 602 


6221. I 


H 


238.368 


4521.5 


Vz 


259.181 


5345-6 


A 


279.994 


6238.6 


76 


238.761 


4536.5 


5/i 


259.574 


5361.8 


H 


280.387 


6256.1 


% 


239-154 


4551.4 


M 


259.967 


5378.1 


% 


280.780 


6273 .7 


H 


239.546 


4566.4 


% 


260.359 


5394.3 


H 


281.173 


6291.2 


3/^ 


239.939 


4581.3 


83 


260.752 


5410.6 


% 


281.565 


6308.8 


H 


240.332 


4596.3 


M 


261 . 145 


5426.9 


3/4 


281.958 


6326.4 


5/8 


240.725 


4611.4 


Vi 


261.538 


5443.3 


li 


282.351 


6344.1 


M 


241. 117 


4626.4 


% 


261.930 


5459-6 


90 


282.743 


6361.7 


% 


241.510 


4641.5 


1/^ 


262.323 


5476.0 


A 


283.136 


6379-4 


77 


241.903 


4656.6 


5/8 


262.716 


5492.4 


M 


283.529 


6397.1 


H 


242.295 


4671.8 


3/4 


263.108 


5508.8 


3/i 


283.921 


6414-9 


H 


242.688 


4686.9 


% 


263 . 501 


5525.3 


A 


284.314 


6432.6 


3^ 


243.081 


4702.1 


84 


263.894 


5541.8 


A 


284.707 


6450.4 


1/^ 


243-473 


4717-3 


\i 


264.286 


5558.3 


3/4 


285.100 


6468.2 


5^ 


243.866 


4732.5 


Vi 


264.679 


5574.8 


''A 


285.492 


6486.0 


% 


244.259 


4747.8 


3,^ 


265.072 


5591-4 


91 


285.88s 


6503.9 


% 


244.652 


4763.1 


/2 


265.465 


5607.9 


A 


286.278 


6521.8 



Areas and Circumferences of Circles 



69 



Areas and Circumferences of Circles for Diameters in 
Units and Eighths, etc. — {Concluded) 



Diam 


Circum- 




Diam 


Circum- 


Area 


Diam- 


Circum- 




eter 


ference 


Area 


eter 


ference 


eter 


ference 


Area 


91 H 


286.670 


6539.7 


94H 


296.095 


6976.7 


97K 


305.520 


7428.0 


% 


287.063 


6557.6 


H 


296.488 


6995.3 


% 


305.913 


7447-1 


Vi 


287.456 


6575.5 


V2 


296.881 


7013.8 


Vi 


306.305 


7466.2 


% 


287.848 


6593.5 


H 


297.273 


7032.4 


A 


306.698 


748s. 3 


H 


288 . 241 


6611.5 


% 


297.666 


7051.0 


% 


307.091 


7504.5 


"A 


288.634 


6629.6 


""A 


298.059 


7069.6 


li 


307.483 


7523.7 


92 


289 . 027 


6647.6 


95 


298.451 


7088.2 


98 


307.876 


7543.0 


H 


289.419 


6665.7 


A 


298.844 


7106.9 


A 


308.269 


7562.2 


H 


289.812 


6683.8 


H 


299.237 


7125.6 


H 


308.661 


7581.5 


H 


290.205 


6701.9 


% 


.299.629 


7144.3 


% 


309.054 


7600.8 


H 


290.597 


6720.1 


V2 


300.022 


7163.0 


1/2 


309.447 


7620.1 


% 


290.990 


6738.2 


% 


300.415 


7181.8 


% 


309.840 


7639.5 


H 


291.383 


6756.4 


% 


300.807 


7200.6 


% 


310.232 


7658.9 


% 


291 . 775 


6774.7 


A 


301 . 200 


7219.4 


'A 


310.625 


7678.3 


93 


292.168 


6792.9 


96 


301.593 


7238.2 


99 


311. 018 


7697.7 


Vs 


292.561 


6811.2 


A 


301.986 


7257.1 


Vs 


311. 410 


7717. I 


Vi 


292.954 


6829. 5 


H 


302.378 


7276.0 


H 


311.803 


7736.6 


% 


293.346 


6847.8 


H 


302.771 


7294.9 


H 


312.196 


7756.1 


H 


293.739 


6866.1 


V2 


303.164 


7313.8 


1/2 


312.588 


7775.6 


% 


294.132 


6884.5 


5/8 


303.556 


7332.8 


% 


312.981 


7795.2 


% 


294.524 


6902.9 


-H 


303.949 


7351.8 


Vi 


313.374 


7814.8 


% 


294.917 


6921.3 


% 


304.342 


7370.8 


A 


313.767 


7834.4 


94 


295.310 


6939.8 


97 


304.734 


7389.8 


100 


314.159 


7854.0 


^ 


295.702 


6958.2 


A 


305.127 


7408.9 









70 



Mathematical Tables 



Areas and Circumferences of Circles for Diameters 
FROM Ho TO loo Advancing by Tenths 



Diameter 


Area 


Circumference Diair 


leter 


Area 


Circumference 


0.6 




s 


3 

4 


22.0618 
22.9022 


16.6504 


.1 


.007854 


.31416 


16.9646 


.2 


.031416 


.62832 


5 


23.7583 


17.2788 


• 3 


.070686 


.94248 


6 


24 - 6301 


17.5929 


.4 


.12566 


1.2566 


7 


25.5176 


17.9071 


.5 


■1963s 


1.5708 


8 


26.4208 


18.2212 


.6 


.28274 


1.8850 


9 


27-3397 


18-5354 


• 7 


.38485 


2.1991 6 





28.2743 


18.8496 


.8 


.50266 


2.S133 


I 


29.2247 


19.1637 


• 9 


.63617 


2.8274 


2 


30.1907 


19-4779 


I.O 


.7854 


3.1416 


3 


31.1725 


19.7920 


.1 


.9503 


3-4558 


4 


32.1699 


20.1062 


.2 


I . 1310 


3-7699 


5 


33.1831 


20.4204 


.3 


1-3273 


4-0841 


6 


34.2119 


20. 7345 


.4 


1.5394 


4.3982 


7 


35.2565 


21.0487 


.5 


I . 7671 


4.7124 


8 


36.3168 


21.3628 


.6 


2.0106 


5.0265 


9 


37.3928 


21.6770 


• 7 


2.2698 


5.3407 7 





38-4845 


21.9911 


.8 


2.5447 


5.6549 


I 


39-5919 


22.3053 


• 9 


2.8353 


5.9690 


2 


40.7150 


22.6195 


2.0 


3.1416 


6.3832 


3 


41-8539 


22.9336 


.1 


3.4636 


6.5973 


4 


43.0084 


23.2478 


.2 


3.8013 


6.911S 


5 


44.1786 


23-5619 


• 3 


4.1548 


7.2257 


6 


45.3646 


23.8761 


■ 4 


4.5239 


7.5398 


7 


46.5663 


24.1903 


• 5 


4.9087 


7.8540 


8 


47.7836 


24-5044 


.6 


5.3093 


8.1681 


9 


49 -0167 


24-8186 


-7 


5.7256 


8.4823 8 





50.2655 


25.1327 


.8 


6.1575 


8.7965 


I 


51.5300 


25.4469 


•9 


6.6052 


9.1106 


2 


52.8102 


25.7611 


3.0 


7.0686 


9-4248 


3 


54.1061 


26.0752 


.1 


7.5477 


9-7389 


4 


55.4177 


26.3894 


.2 


8.0425 


10.0531 


5 


56.7450 


26.7035 


.3 


8.5530 


10.3673 


6 


58.0880 


27.0177 


.4 


9 0792 


10.6814 


7 


59.4468 


27.3319 


.5 


9.6211 


10.9956 


8 


60.8212 


27.6460 


.6 


10.1788 


11.3097 


9 


62.2114 


27.9602 


.7 


10.7521 


11.6239 9 





63.6173 


28.2743 


.8 


II. 341 I 


I I. 9381 


I 


65.0388 


28.588s 


•9 


11.9459 


12.2522 


2 


66.4761 


28.9027 


4.0 


12.5664 


12.5664 


3 


67.9291 


29.2168 


.1 


13.202s 


12.8805 


4 


69.3978 


29.5310 


.2 


13.8544 


13.1947 


5 


70.8822 


29.8451 


.3 


14.5220 


13.5088 


6 


72.3823 


30.1593 


• 4 


15.2053 


13.8230 


7 


73.8981 


30.4734 


.5 


15.9043 


14.1372 


8 


75.4296 


30.7876 


.6 


16.6190 


14.4513 


9 


76.9769 


31 . 1018 


• 7 


17.3494 


14.765s 10 





78.5398 


31.4159 


.8 


18.0956 


15.0796 


I 


80.1185 


31.7301 


• 9 


18.8574 


15.3938 


2 


81.7128 


32.0442 


S.o 


19-6350 


IS. 7080 


3 


. 83.3229 


32.3584 


.1 


20.4282 


16.0221 


4 


84.9487 


32.6726 


.2 


21.2372 


16.3363 


5 


86.5901 


32.9867 



Areas and Circumferences of Circles 



71 



Areas and Circumferences of Circles for Diameters 
FROM Mo to 100 Advancing by Tenths — {Continued) 



Diameter 


Area 


Circumference 


Diameter 


Area 


Circumference 


10.6 


88.2473 


33.3009 


15.9 


198.5565 


49.9513 


.7 


89.9202 


33.6150 


16.0 


201.0619 


50.2655 


.8 


91.6088 


33.9292 


.1 


203.5831 


50.5796 


.9 


93.3132 


34.2434 


.2 


206.1199 


so. 8938 


«.o 


95.0332 


34.5575 


.3 


208.6724 


SI. 2080 




96.7689 


34.8717 


.4 


211.2407 


51.5221 


.2 


98.5203 


35.1858 


.5 


213.8246 


SI. 8363 


.3 


100.2875 


35.5000 


.6 


216.4243 


52.1504 


• 4 


102.0703 


35.8142 


.7 


219.0397 


52.4646 


.5 


103.8689 


36.1283 


.8 


221.6708 


52.7788 


.6 


105.6832 


36.442s 


• 9 


224.3176 


53.0929 


.7 


107.5132 


36.7566 


17.0 


226.9801 


53.4071 


.8 


109.3588 


37.0708 


.1 


229.6583 


53.7212 


• 9 


III. 2202 


37.3850 


.2 


232.3522 


54.0354 


12.0 


113.0973 


37.6991 


.3 


235.0618 


54.3496 


.1 


114. 9901 


38.0133 


.4 


237.7871 


54.6637 


.2 


116.8987 


38.3274 


.5 


240.5282 


54.9779 


.3 


118.8229 


38.6416 


.6 


243.2849 


55.2920 


.4 


120.7628 


38.9557 


.7 


246.0574 


55.6062 


.5 


122.7185 


39.2699 


.8 


248.8456 


55.9203 


.6 


124.6898 


39.5841 


• 9 


251.6494 


56.2345 


•7 


126.6769 


39.8982 


18.0 


254.4690 


56.5486 


.8 


128.6796 


40.2124 


.1 


257.3043 


56.8628 


• 9 


130.6981 


40.5265 


.2 


260.1553 


57 . 1770 


13.0 


132.7323 


40.8407 


.3 


263.0220 


57.4911 


.1 


134.7822 


41.1549 


■ 4 


265.9044 


57.8053 


.2 


136.8478 


41.4690 


■ 5 


268.8025 


58.119s 


.3 


138.9291 


41.7832 


.6 


271.7164 


58.4336 


• 4 


141. 0261 


42.0973 


.7 


274.6459 


58.7478 


.5 


143.1388 


42.4115 


.8 


277.5911 


59.0619 


.6 


145.2672 


42.7257 


■9 


280.5521 


59.3761 


.7 


147.4114 


43.0398 


19.0 


283.5287 


59.6903 


.8 


149.5712 


43.3540 


.1 


286.5211 


60.0044 


• 9 


151.7468 


43.6681 


.2 


289.5292 


60.3186 


14.0 


153.9380 


43.9823 


.3 


292.5530 


60.6327 


.1 


156.1450 


44.2965 


.4 


295.592s 


60.9469 


.2 


158.3677 


44.6106 


.5 


298.6477 


61.2611 


•3 


160.6061 


44.9248 


.6 


301.7186 


61.5752 


.4 


162.8602 


45.2389 


.7 


304.8052 


61.8894 


■ 5 


165 . 1300 


45.5531 


.8 


307.907s 


62.203s 


.6 


167.4155 


45.8673 


• 9 


311.0255 


62.S177 


.7 


169.7167 


46.1814 


20.0 


314.1593 


62.8319 


.8 


172.0336 


46.4956 


.1 


317.3087 


63 . 1460 


• 9 


174.3662 


46.8097 


.2 


320.4739 


63.4602 


iS.o 


176.7146 


47.1239 


.3 


323.6547 


63.7743 


.1 


179.0786 


47.4380 


.4 


326.8513 


64.088s 


.2 


181.4584 


47.7522 


.5 


330.0636 


64.4026 


.3 


183.8539 


48.0664 


.6 


333.2916 


64.7168 


.4 


186.2650 


48.3805 


.7 


336.5353 


65.03x0 


.5 


188.6919 


48.6947 


.8 


339.7947 


65.3451 


.6 


191 . 1345 


49.0088 


•9 


343.0698 


65.6593 


.7 


193.5928 


49.3230 


21.0 


346.3606 


65.9734 


.8 


196.0668 


49.6372 


.1 


349.6671 


66.2876 



72 



Mathematical Tables 



Aeeas and Circumferences of Circles for Diameters 
FROM Mo TO loo Advancing by Tenths — (Continued) 



Diameter 


Area 


Circumference Diair 


leter 


Area 


Circumference 


21.2 


352.9894 


66.6018 26 


5 


551.5459 


83.2522 




3 


356.3273 


66.9159 


6 


555.7163 


83 


S664 




4 


359 6809 


67.2301 


7 


559.9025 


83 


8805 




5 


363.0503 


67.5442 


8 


564.1044 


84 


1947 




6 


366 . 4354 


67.8584 


9. 


568.3220 


84 


5088 




7 


369.8361 


68.1726 27 





572.5553 


84 


8230 




8 


373 • 2526 


68.4867 


I 


576.8043 


85 


1372 




9 


376.6848 


68.8009 


2 


581.0690 


85 


4513 


22 


o 


380.1327 


69.1150 


3 


585.3494 


85 


7655 




I 


383.5963 


69.4292 


.4 


589.6455 


86 


0796 




2 


387.0756 ■ 


69.7434 


.5 


593.9574 


86 


3938 




3 


390.5707 


70.0575 


.6 


598.2849 


86 


7080 




.4 


394.0814 


70.3717 


.7 


602.6282 


87 


0221 




• 5 


397.6078 


70.6858 


.8 


606.9871 


87 


3363 




.6 


401 . 1500 


71.0000 


.9 


61 I. 3618 


87 


6504 




• 7 


404.7078 


71.3142 28 


.0 


615.7522 


87 


9646 




.8 


408 . 2814 


71.6283 


.1 


620.1582 


88 


2788 




■ 9 


411.8707 


71.9425 


.2 


624.5800 


88 


5929 


23 


.o 


415.4756 


72.2566 


.3 


629.017s 


88 


9071 




.1 


419.0963 


72.5708 


.4 


633.4707 


89 


.2212 




.2 


422.7327 


72.8849 


.5 


637.9397 


89 


.5354 




.3 


426.3848 


73.1991 


.6 


642.4243 


89 


.8495 




• 4 


430.0526 


73.5133 


.7 


646 . 9246 


90 


.1637 




.5 


433.7361 


73.8274 


.8 


651.4407 


90 


.4779 




.6 


437.4354 


74.1416 


•9 


655.9724 


90 


.7920 




■ 7 


441 . 1503 


74.4557 29 


.0 


660.5199 


91 


.1062 




.8 


444.8809 


74.7699 


.1 


665.0830 


91 


.4203 




9 


448.6273 


75.0841 


.2 


669.6619 


91 


.7345 


24 


o 


452.3893 


75.3892 


• 3 


674.2565 


92 


.0487 




I 


456 . 1671 


75.7124 


.4 


678.8668 


92 


.3628 




2 


459.9606 


76.0265 


•5 


683 . 4928 


92 


6770 




3 


463.7698 


76.3407 


.6 


688.1345 


92 


991 1 




4 


467.5947 


76.6549 


.7 


692.7919 


93 


3053 




5 


471.4352 


76.9690 


.8 


697.4650 


93 


6195 




6 


475 . 2916 


77.2832 


9 


702 . 1538 


93 


9336 




7 


479.1636 


77.5973 30 





706.8583 


94 


2478 




8 


483.0513 


77.9115 


I 


711.5786 


94 


5619 




9 


486.9547 


78.2257 


2 


716.314s 


94 


8761 


25 


o 


490.8739 


78.5398 


3 


721.0662 


95 


1903 




I 


494.8087 


78.8540 


4 


725.8336 


95 


5044 




2 


498.7592 


79.1681 


5 


730.6167 


95 


8186 




3 


502 . 7255 


79.4823 


6 


735.4154 


96 


1327 




4 


506.7075 


79.796s 


7 


740.2299 


96 


4469 




5 


510.7052 


80.1106 


8 


745.0601 


96 


761 1 




6 


514.7185 


80.4248 


9 


749.9060 


97 


0752 




7 


S18.7476 


80.7389 31 





754.7676 


97 


3894 




8 


522.7924 


81.0531 


I 


759.6450 


97 


7035 




9 


526.8529 


81.3672 


2 


764.5380 


98 


0177 


26. 


o 


530.9292 


81.6814 


3 


769.4467 


98 


3319 




I 


S35.02II 


81.9956 


4 


774.3712 


98 


6460 




2 


539.1287 


82.3097 


5 


779.3113 


98 


9602 




3 


543.2521 


82.6239 


6 


784.2672 


99 


2743 




4 


547. 391 I 


82.9380 


7 


789.2388 


99. 


5885 



Areas and Circumferences of Circles 



73 



Areas and Circumferences of Circles for Diameters 
FROM Ho TO loo Advancing by Tenths — {Continued) 



Diameter 


Area 


Circumference Diarr 


eter 


Area 


Circumference 


31.8 


794-2260 


99.9026 37. 


I 


1081.0299 


116. 5531 




9 


799 2290 


100.2168 


2 


1086.8654 


116.8672 


32. 


o 


804.2477 


100.5310 


3 


1092. 7166 


117.1814 




I 


809.2821 


100.8451 


4 


1098.5835 


117.4956 




2 


814.3322 


101.1593 


5 


I 104. 4662 


117.8097 




3 


819.3980 


101.4734 


6 


mo. 3645 


118. 1239 




4 


824.4796 


101.7876 


7 


1116.2786 


118.4380 




5 


829.5768 


102 . 1018 


8 


I 122. 2083 


118.7522 




6 


834.6898 


102.4159 


9 


I 128. 1538 


119.0664 




7 


839.8185 


102 . 7301 38 





1134.1149 


119.3805 




8 


844.9628 


103.0442 


I 


1140.0918 


119.6947 




9 


850.1229 


103.3584 


2 


I 146. 0844 


120.0088 


33 


o 


855.2986 


103.6726 


3 


I 152. 0927 


120.3230 




I 


860.4902 


103.9867 


4 


1158.1167 


120.6372 




2 


865.6973 


104 . 3009 


5 


1164.1564 


120.9513 




3 


870.9202 


104.6150 


6 


1170.2118 


121.2655 




4 


876.1588 


104.9292 


7 


I 176. 2830 


121.5796 




S 


881.4131 


105 . 2434 


8 


I 182. 3698 


121.8938 




6 


886.6831 


105.5575 


9 


I 188. 4724 


122 . 2080 




7 


891.9688 


105.8717 39 





I 194. 5906 


122.5221 




8 


897.2703 


106.1858 


I 


1200.7246 


122.8363 




9 


902.5874 


106 . 5000 


2 


1206.8742 


123.1504 


34 


o 


907.9203 


106.8142 


3 


1213.0396 


123.4646 




I 


913.2688 


107.1283 


4 


1219.2207 


123.7788 




2 


918.6331 


107.4425 


5 


1225. 4175 


124.0929 




3 


924.0131 


107.7566 


6 


1231.6300 


124.4071 




4 


929.4088 


108.0708 


7 


1237.8582 


124.7212 




5 


934.8202 


108.3849 


8 


1244. 1021 


125.0354 




6 


940.2473 


108.6991 


9 


1250. 3617 


125.3495 




7 


945.6901 


109.0133 40 





1256. 6371 


125.6637 




8 


951.1486 


109.3274 


I 


1262. 9281 


125.9779 




9 


956.6228 


109.6416 


2 


1269.2348 


126.2920 


35 


o 


962.1128 


109.9557 


3 


1275.5573 


126.6062 




I 


967.6184 


110.2699 


4 


1281.8955 


126.9203 




2 


973.1397 


no. 5841 


5 


1288.2493 


127.2345 




3 


978 . 6768 


110.8982 


.6 


1294. 6189 


127.5487 




4 


984.2296 


III. 2124 


7 


1301.0042 


127.8628 




5 


989.7980 


III. 5265 


8 


1307 . 4052 


128.1770 




.6 


995.3822 


II I. 8407 


9 


1313.8219 


128. 491 I 




.7 


1000. 9821 


112. 1549 41 


.0 


1320.2543 


128.8053 




.8 


1006.5977 


112.4690 


.1 


1326.7024 


129. I 195 




• 9 


1012 . 2290 


112.7832 


.2 


1333. 1663 


129.4336 


36 


o 


1017.8760 


113.0973 


.3 


1339.6458 


129.7478 




.1 


1023.5387 


113.4115 


4 


1346 . 1410 


130.0619 




.2 


1029. 2172 


113.7257 


5 


1352 . 6520 


130.3761 




.3 


1034. 91 13 


114.0398 


.6 


1359. 1786 


130.6903 




• 4 


1040. 6212 


114.3540- 


.7 


1365. 7210 


131.0044 




.5 


1046.3467 


114. 6681 


.8 


1372. 2791 


131. 3186 




.6 


1052.0880 


114.9823 


■ 9 


1378.8529 


131.6327 




.7 


1057.8449 


115.2965 42 


.0 


1385.4424 


131.9469 




.8 


1063. 6176 


115. 6106 


.1 


1392.0476 


132. 261 I 




•9 


1069.4060 


115.9248 


.2 


1398.6685 


132.5752 


37. o 


1075. 2 lOI 


116.2389 


.3 


140S.3051 


132.8894 



74 



Mathematical Tables 



Areas and Circumferences of Circles for Diameters 
FROM Mo TO loo Advancing by Tenths — {Continued) 



Diameter 


Area 


Circumference Diarr 


leter 


Area 


Circumference 


42.4 


141 I. 9574 


133.2035 47 


7 


1787.0086 


149-8540 




5 


1418.6254 


133-5177 


8 


1794.5091 


150.1681 




6 


1425.3092 


133.8318 


9 


1802.0254 


150.4823 




7 


1432.0086 


134.1460 48 





1809.5574 


150.7964 




8 


1438.7238 


134.4602 


I 


1817.1050 


151.1106 




9 


1445.4546 


134.7743 


2 


1824.6684 


ISI.4248 


43 





1452 . 2012 


135.0885 


3 


1832 . 2475 


151.7389 




I 


1458.9635 


135.4026 


4 


1839.8423 


152.0531 




2 


1465. 741S . 


135.7168 


5- 


1847.4528 


152.3672 




3 


1472.5352 


136.0310 


6 


1855 -0790 


152.6814 




4 


1479-3446 


136.3451 


7 


1862. 7210 


152.9956 




5 


i486. 1697 


136.6593 


8 


1870 . 3786 


153-3097 




6 


1493 oios 


136.9734 


9 


1878. 0519 


153.6239 




7 


1499-8670 


137.2876 49 





1885.7409 


153.9380 




8 


1506.7393 


137.6018 


I 


1893.4457 


154-2522 




9 


1513-6272 


137-9159 


2 


1901 . 1662 


154-5664 


44 





1520.5308 


138.2301 


3 


1908.9024 


154-8805 




I 


1527.4502 


138.5442 


4 


1916.6543 


155.1947 




2 


1534.3853 


138.8584 


5 


1924. 4218 


155-5088 




3 


154I-3360 


139-1726 


6 


1932 . 2051 


155-8230 




4 


1548.3025 


139-4867 


7 


1940.0042 


156.1372 




5 


1555-2847 


139-8009 


8 


1947. 8189 


156.4513 




6 


1562.2826 


140.1153 


9 


1955.6493 


156.7655 




7 


1569.2962 


140.4292 So 





1963-4954 


157-0796 




8 


1576.3255 


140.7434 


I 


1971.3572 


157.3938 




9 


1583.3706 


141.0575 


2 


1979.2348 


157.7080 


45 





1590. 4313 


141. 3717 


3 


1987 . 1280 


158.0221 




I 


1597.5077 


141.6858 


4 


1995-0370 


158.3363 




2 


1604.5999 


142.0000 


5 


2002.9617 


158.6504 




3 


1611.7077 


142.3142 


6 


2010 . 9020 


158.9646 




4 


1618.8313 


142.6283 


7 


2018. 8581 


159-2787 




5 


1625.9705 


142.9425 


8 


2026.8299 


159-5929 




6 


1633. 1255 


143.2566 


9 


2034-8174 


159-9071 




7 


1640.2962 


143.5708 51 





2042.8206 


160.2212 




8 


1647.4826 


143.8849 


I 


2050.839s 


160.5354 




9 


1654.6847 


144.1991 


2 


2058.8742 


160.849s 


46 





1661.9025 


144.5133 


3 


2066.9245 


161 . 1637 




I 


1669. 1360 


144.8274 


4 


2074.990s 


161.4779 




2 


1676.3853 


145.1416 


5 


2083.0723 


161.7920 




3 


1683.6502 


145-4557 


6 


2091 . 1697 


162.1062 




4 


1690.9308 


145.7699 


7 


2099.2829 


162.4203 




5 


1698.2272 


146.0841 


8 


2107. 4118 


162.734s 




6 


170S.5392 


146.3982 


9 


21 15. 5563 


163.0487 




7- 


1712.8670 


146.7124 52 





2123. 7166 


163.3628 




.8 


1720. 2105 


147.0265 


I 


2131.8926 


163.6770 




•9 


1727.5697 


147.3407 


2 


2140.0843 


163.9911 


47 





1734.9445 


147.6550 


3 


2148. 2917 


164.3053 




.1 


1742. 3351 


147.9690 


4 


2156.5149 


164.6195 




.2 


1749. 7414 


148.2832 


5 


2164.7537 


164.9336 




.3 


1757. 1635 


148.5973 


6 


2173.0082 


165.2479 




.4 


1764. 6012 


148.9115 


7 


2181.2785 


165.5619 




.5 


1772.0546 


149.2257 


8 


2189.5644 


165.8761 


.6 


1779.5237 


149.5398 


9 


2197. 8661 


166.1903 



Areas and Circiimferences of Circles 



7^ 



Areas and Circumferences of Circles for Diameters 
FROM Ho to ioo Advancing by Tenths — {Continued) 



Diameter 


Area 


Circumference 


Diameter 


Area 


Circumference 


53. o 


2206.1834 


166.5044 


58.3 


2669.4820 


183.5914 


.1 


2214. 5165 


166.8186 


.4 


2678.6476 


183.4690 


.2 


2222 . 8653 


167.1327 


.5 


2687.8289 


183.7832 


.3 


2231 . 2298 


167.4469 


6 


2697.0259 


184.0973 


• 4 


2239 . 6100 


167.7610 


.7 


2706.2386 


184.411S 


.5 


2248.0059 


168.0752 


.8 


2715.4670 


184.7256 


. .6 


2256.4175 


168.3894 


• 9 


2724. 7112 


185.0398 


.7 


2264.8448 


168.703s 


59.0 


2733.9710 


185.3540 


.8 


2273.2879 


169.0177 


.1 


2743.2466 


185.6681 


.9 


2281.7466 


169.3318 


.2 


2752.5378 


185.9823 


54. o 


2290.2210 


169 . 6460 


.3 


2761.8448 


186.2964 


.1 


2298. 7112 


169.9602 


.4 


2771. 1675 


186.6106 


.2 


2307. 2171 


170.2743 


.5 


2780.5058 


186.9248 


.3 


231S.7386 


170.5885 


.6 


2789.8599 


187.2389 


• 4 


2324.2759 


170.9026 


.7 


2799.2297 


187.5531 


.5 


2332.8289 


171. 2168 


.8 


2808.6152 


187.8672 


.6 


2341.3976 


171. 5310 


• 9 


2818. 0165 


188.1814 


• 7 


2349.9820 


171. 8451 


60.0 


2827.4334 


188.4956 


.8 


2358.5821 


172.1593 


.1 


2836.8660 


188.8097 


•9 


2367 . 1979 


172.4735 


.2 


2S46.3144 


189.1239 


55. o 


2375.8294 


172.7876 


.3 


2855.7784 


189.4380 


.1 


2384.4767 


173.1017 


.4 


286s . 2582 


189.7522 


.2 


2393.1396 


173.4159 


.5 


2874.7536 


190.0664 


.3 


2401. 8183 


173.7301 


.6 


2884.2648 


190.3805 


• 4 


2410. 5126 


174.0442 


.7 


2893.7917 


190.6947 


.5 


2419.2227 


174.3584 


.8 


2903.3343 


191.0088 


.6 


2427.9485 


174.6726 


• 9 


2912.8926 


191.3230 


.7 


2436.6899 


174.9867 


61.0 


2922.4666 


191.6372 


.8 


2445.4471 


175.3009 


.1 


2932.0563 


191. 9513 


•9 


2454.2200 


175.6150 


.2 


2941. 6617 


192.2655 


56.0 


2463.0086 


175.9292 


3 


2951 . 2828 


192.5796 


.1 


2471. 8130 


176.2433 


4 


2960.9197 


192.8938 


.2 


2480.6330 


176.5575 


5 


2970.5722 


193.2079 


.3 


2489.4687 


176.8717 


6 


2980.2405 


193.5221 


.4 


2498.3201 


177.1858 


■ 7 


2989.9244 


193.8363 


.5 


2507.1873 


177.5000 


.8 


2999.6241 


194.1504 


.6 


2516. 0701 


177.8141 


• 9 


3009.3395 


194.4646 


.7 


2524.9687 


178.1283 


62.0 


3019.0705 


194.7787 


.8 


2533.8830 


178.4425 


.1 


3028.8173 


195.0929 


.9 


2542.8129 


178.7566 


.2 


3038.5798 


195.4071 


57. 


2551.7586 


179.0708 


.3 


3048.3580 


195.7212 


.1 


2560.7200 


179.3849 


.4 


3058.1520 


196.0354 


.2 


2569.6971 


179.6991 


.5 


3067.9616 


196.349s 


.3 


2578.6899 


180.0133 


.6 


3077.7869 


196.6637 


.4 


2587.6985 


180.3274 


.7 


3087.6279 


196.9779 


.5 


2596.7227 


180.6416 - 


.8 


3097.4847 


197.2920 


.6 


2605.7626 


180.9557 


•9 


3107. 3571 


197.6062 


.7 


2614. 8183 


181.2699 


63.0 


3117.2453 


197.9203 


.8 


2623.8896 


181. 5841 


.1 


3127. 1492 


198.2345 


•9 


2632 . 9767 


181 , 8982 


.2 


3137.0688 


198.5487 


S8.0 


2642.0794 


182.2124 


.3 


3147.0040 


198.8628 


.1 


2651 . 1979 


182.5265 


.4 


3156.9550 


199.1770 


.2 


2660.3321 


182.8407 


.5 


3166. 9217 


199.4911 



76 



Mathematical Tables 



Areas and Circumferences of Circles for Diameters 
FROM Ho TO loo Advancing by Tenths — (Continued) 



Diameter 


Area 


1 
Circumference Diam 


eter 


Area 


Circumference 


63.6 


3176.9043 


199.8053 68 


9 


3728.4500 


216.4556 




7 


3186.9023 


200.1195 69 





3739.2807 


216.7699 




8 


3196 . 9161 


200.4336 


I 


3750.1270 


217.0841 




9 


3206.9456 


200.7478 


2 


3760.9891 


217.3982 


64 





3216.9909 


201.0620 


3 


3771.8668 


217.7124 




I 


3227.0518 


201.3761 


4 


3782.7603 


218.0265 




2 


3237 . 128s 


201 . 6902 


5 


3793.669s 


218.3407 




3 


3247 ■ 2222 


202.0044 


6 


3804.5944 


218.6548 




4 


3257.3289 . 


202.3186 


7 


3815.5350 


218.9690 




5 


3267.4527- 


202.6327 


8 


3826.4913 


219.2832 




6 


3277.5922 


202.9469 


9 


3837 • 4633 


219.5973 




7 


3287.7474 


203.2610 70 





3848.4510 


219.9115 




8 


3297.9183 


203.5752 


I 


3859.4544 


220.2256 




9 


3308.1049 


203.8894 


2 


3870.4736 


220.5398 


65 





3318.3072 


204.2035 


3 


3881. S084 


220.8540 




I 


3328.5253 


204.5176 


4 


3892.5590 


221.1581 




2 


3338.7590 


204.8318 


5 


3903.6252 


221.4823 




3 


3349.008s 


205.1460 


6 


3914.7072 


221.7964 




4 


3359-2736 


205.4602 


7 


3925.8049 


222.1106 




5 


3369.5545 


205.7743 


8 


3936.9182 


222 . 4248 




6 


3379.8510 


206.0885 


9 


3948.0473 


222.7389 




7 


3390.1633 


206.4026 71 





3959.1921 


223.0531 




8 


3400.4913 


206.7168 


I 


3970.3526 


223.3672 




9 


3410.8350 


207.0310 


2 


3981.5289 


223.6814 


66 





3421 . 1944 


207.3451 


3 


3992.7208 


223.9956 




.1 


3431.5695 


207.6593 


4 


4003.9284 


224.3097 




.2 


3441.9603 


207.9734 


5 


4015. 1518 


224.6239 




.3 


3452.3669 


208.2876 


6 


4026.3908 


224.9380 




.4 


3462.7891 


208.6017 


.7 


4037 . 6456 


225.2522 , 




.5 


3473.2270 


208.9159 


.8 


4048.9160 


225.5664 




.6 


3483.6807 


209 . 2301 


9 


4060.2022 


225.8805 




.7 


3494. iSoo 


209.5442 72 





4071. 5041 


226 . 1947 




.8 


3504.6351 


209.8584 


.1 


4082.8217 


226.5088 




.9 


3515. 1359 


210.1725 


.2 


4094.1550 


226.8230 


■ 67 


.0 


3525.6524 


210.4867 


.3 


4105.5040 


227.1371 




.1 


3536.1845 


210.8009 


■4 


41 16. 8687 


227.4513 




.2 


3546.7324 


211.1150 


.5 


4128. 2491 


227.765s 




.3 


3557 . 2960 


211.4292 


.6 


4139.6452 


228.0796 




•4 


3567.8754 


211.7433 


.7 


4151.0571 


228.3938 




.5 


3578.4704 


212.0575 


.8 


4162 . 4846 


228 . 7079 




.6 


3589. 0811 


212.3717 


• 9 


4173.9279 


229.0221 




•7 


3599.7075 


212.6858 73 





4185.3868 


229.3363 




.8 


3610.3497 


213.0000 


.1 


4196. 861S 


229.6504 




• 9 


3621.0075 


213.3141 


.2 


4208.3519 


229.9646 


68 


.0 


3631. 6811 


213.6283 


.3 


4219.8579 


230.2787 




.1 


3642.3704 


213.9425 


• 4 


4231.3797 


230.5929 




.2 


3653.0754 


214.2566 


.5 


4242.9172 


230.9071 




.3 


3663.7960 


214.5708 


.6 


4254.4704 


231.2212 




•4 


3674.5324 


214.8849 


.7 


4266.0394 


231.5354 




.5 


3685.2845 


215.1991 


.8 


4277.6240 


231.849s 




.6 


3696.0523 


215.5133 


.9 


4289.2243 


232.1637 




• 7 


3706.8359 


215.8274 74 





4300.8403 


232.4779 




.8 


3717. 6351 


216.1416 


.1 


4312. 4721 


232.7920 



Areas and Circumferences of Circles 



77 



Areas and Circumferences of Circles for Diameters 
FROM Mo TO loo Advancing by Tenths — {Continued) 



Diameter 


Area 


Circumference Dian 


aeter 


Area 


Circumference 


74.2 


4324. II95 


233.1062 79 


5 


4963.9127 


249.7566 




3 


4335.7827 


233.4203 


6 


4976.4084 


250.0708 




4 


4347.4616 


233.7345 


7 


4988.9198 


250.3850 




5 


4359.1562 


234.0487 


8 


5001 . 4469 


250.6991 




6 


4370.8664 


234.3628 


9 


5013 . 9897 


251.0133 




7 


4382.5924 


234.6770 80 





5026 . 5482 


251.3274 




8 


4394-3341 


234.9911 


I 


5039.1225 


251.6416 




9 


4406.0916 


235.3053 


2 


5051 . 7124 


251.9557 


75 


o 


4417.8647 


235.6194 


3 


5064.3180 


252.2699 




I 


4429.6535 


235.9336 


4 


5076.9394 


252.5840 




2 


4441 4580 


236.2478 


5 


5089.5764 


252.8982 




3 


4453.2783 


236.5619 


6 


5102 . 2292 


253.2124 




4 


4465. I 142 


236.8761 


7 


5114.8977 


253.5265 




5 


4476.9659 


237.1902 


8 


5127. 5819 


253.8407 




6 


4488.8332 


237.5044 


9 


5140. 2818 


254.1548 




7 


4500.7163 


237.8186 81 





5152.9973 


254.4690 




8 


4512. 6151 


238.1327 


I 


5165.7287 


254 7832 




9 


4524.5296 


238.4469 


2 


5178.4757 


255.0973 


76 


o 


4536.4598 


238 . 7610 


3 


5191 . 2384 


255. 41 IS 




I 


4548.4057 


239.0752 


4 


5204.0168 


255.7256 




2 


4560.3673 


239.3894 


5 


5216. 8110 


256.0398 




3 


4572.3446 


239.7035 


6 


5229 . 6208 


256.3540 




4 


4584.3377 


240.0177 


7 


5242 . 4463 


256.6681 




5 


4596.3464 


240.3318 


8 


5255 . 2876 


256.9823 




6 


4608.3708 


240.6460 


9 


5268.1446 


257.2966 




7 


4620. 41 10 


240.9602 82 





5281. 0173 


257.6106 




8 


4632 . 4669 


241.2743 


I . 


5293.9056 


257.9247 




9 


4644.5384 


241.5885 


2 


5306.8097 


258.2389 


77 


o 


4656.6257 


241 . 9026 


3 


5319.7295 


258.5531 




I 


4668.7287 


242.2168 


4 


5332.6650 


258.8672 




2 


4680.8474 


242.5310 


5 


5345.6162 


259.1814 




3 


4692.9818 


242.8451 


6 


5358.5832 


259.4956 




4 


4705 . 1319 


243.1592 


7 


5371.5658 


259.8097 




5 


4717.2977 


243.4734 


8 


5384.5641 


260.1239 




6 


4729.4792 


243.7876 


9 


5397.5782 


260.4380 




7 


4741.6756 


244.1017 83 





5410.6079 


260.7522 




8 


4753.8894 


244.4159 


I 


5423.6534 


261.0663 




9 


4766. 1181 


244.7301 


2 


5436.7146 


261. 380s 


78 


o 


4778.3624 


245.0442 


3 


5449.7915 


261.6947 




I 


4790.6225 


245.3584 


4 


5462.8840 


262.0088 




2 


4802.8983 


245.6725 


5 


5475.9923 


262.3230 




3 


4815. 1897 


245.9867 


6 


5489.1163 


262.6371 




4 


4827.4969 


246.3009 


7 


5502 . 2561 


262.9513 




5 


4839.8198 


246.6150 


8 


5515. 4115 


263.265s 




6 


4852.1584 


246.9292 


9 


5528.5826 


263.5796 




7 


4864 . 5128 


247.2433 84 





5541.7694 


263.8938 




8 


4876.8828 


247.5575 


I 


5554.9720 


264.2079 




9 


4889.2685 


247.8717 


2 


5568.1902 


264.5221 


79 


o 


4901.6699 


248.1858 


3 


5581.4242 


264.8363 




I 


4914. 0871 


248.5000 


4 


5594.6739 


265 . 1414 




2 


4926.5199 


248.8141 


5 


5607.9392 


265 . 4646 




3 


4938.9685 


249.1283 


6 


5621.2203 


265.7787 




4 


4951.4328 


249.4425 


7 


5634. 5171 


266.0929 



78 



Mathematical Tables 



Areas and Circumferences of Circles for Diameters 
FROM Ho TO loo Advancing by Tenths — {Continued) 



Diameter 


Area 


Circumference Diarr 


leter 


Area 


Circumference 


84.8 


5647.8296 


266.4071 90 


I 


6375.8701 


283.057s 




9 


5661 . 1578 


266.7212 


2 


_ 6390.0309 


283.3717 


85 ; 





5674-5017 


267.0354 


3 


6404.2073 


283.6858 




I 


5687.8614 


267.349s 


4 


6418.3995 


284.0000 




2 


5701 . 2367 


267.6637 


5 


6432.6073 


284.3141 




3 


5714.6277 


267.9779 


6 


6446.8309 


284.6283 




4 


5728.0345 


268.2920 


7 


6461. 0701 


284.942s 




S 


5741.4569 


268.6062 


8 


6475.3251 


285.2566 




6 


5754.8951 


268.9203 


9 


6489.5958 


285.5708 




7 


5768.3490 


269.2345 91 





6503.8822 


285.8849 




8 


5781. 8185 


269.5486 


I 


6518. 1843 


286.1991 




9 


5795.3038 


269.8628 


2 


6532 . 5021 


286.5133 


86 





5808.8048 


270.1770 


3 


6546.8356 


286.8274 




I 


5822.3215 


270.4911 


4 


6561 . 1848 


287 . 1416 




2 


5835.8539 


270.8053 


5 


6575.5498 


287.4557 




3 


5849.4020 


271.1194 


6 


6589.9304 


287.7699 




4 


5862.9659 


271.4336 


7 


6604.3268 


288.0840 




5 


5876.5454 


271.7478 


8 


6618.7388 


288.3982 




6 


5890.1407 


272.0619 


9 


6633.1666 


288.7124 




7 


5903.7516 


272.3761 92 





6647. 6101 


289.0265 




8 


5917.3783 


272 . 6902 


I 


6662.0692 


289.3407 




9 


5931.0206 


273.0044 


2 


6676.5441 


289.6548 


87 





5944.6787 


273.3186 


3 


6691.0347 


289.9690 




I 


5958.3525 


273.6327 


4 


6705.5410 


290.2832 




2 


5972.0420 


273.9469 


5 


6720.0630 


290.5973 




3 


5985.7472 


274.2610 


6 


6734.6008 


290.9115 




4 


5999.4681 


274.5752 


7 


6749.1542 


291 . 2256 




5 


6013.2047 


274.8894 


8 


6763.7233 


291.5398 




6 


6026 . 9570 


275.2035 


9 


6778.3082 


291.8540 




7 


6040.7250 


275.5177 93 





6792.9087 


292.1681 




8 


6054.5088 


275.8318 


I 


6807.5250 


292.4823 




9 


6068.3082 


276.1460 


2 


6822 . 1569 


292.7964 


88 





6082 . 1234 


276.4602 


3 


6836.8046 


293.1106 




I 


6095.9542 


276.7743 


4 


6851.4680 


293.4248 




2 


6109.8008 


277.0885 


5 


6866. 1471 


293.7389 




3 


6123. 6631 


277.4026 


6 


6880.8419 


294.0531 




4 


6137. 5411 


277.7168 


7 


6895.5524 


294.3672 




5 


6151.4348 


278.0309 


8 


6910.2786 


294.6814 




6 


6165.3442 


278.3451 


9 


6925.0205 


294.9956 




7 


6179.2693 


278.6593 94 





6939.7782 


295.3097 




8 


6193. 2101 


278.9740 


I 


6954.5515 


295.6239 




9 


6207 . 1666 


279.2876 


2 


6969.3106 


295.9380 


89 





6221 . 1389 


279.6017 


3 


6984.1453 


296.2522 




I 


6235 . 1268 


279.9159 


4 


6998.9658 


296.5663 




.2 


6249.1304 


280.2301 


5 


7013. 8019 


296.8805 




.3 


6263 . 1498 


280.5442 


6 


7028.6538 


297.1947 




.4 


6277.1849 


280.8584 


7 


7043.5214 


297.5088 




5 


6291 . 2356 


281 . 1725 


.8 


7058.4047 


297.8230 




.6 


6305.3021 


281.4867 


•9 


7073.3033 


298.1371 




•7 


6319.3843 


281.8009 95 





7088 . 2184 


298.4513 




.8 


6333.4822 


282.1150 


.1 


7103. 1488 


298.765s 




•9 


6347.5958 


282.4292 


.2 


71 18. 1950 


299.0796 


90 


.0 


6361 . 7251 


282.7433 


.3 


7133.0568 


299.3938 



Areas and Circumferences of Circles 



79 



Areas and Circumferences of Circles for Diameters 
FROM Ho TO loo Advancing by Tenths — {Concluded) 



Diameter 


Area 


Circumference Dian 


leter 


Area 


Circumference 


95.4 


7148.0343 


299.7079 97 


8 


7512.2078 


397.2478 




5 


7163.0276 


300.0221 


9 


7527.5780 


307.5619 




6 


7178.0366 


300.3363 98 





7542.9640 


307.8761 




7 


7193. 0612 


300.6504 


I 


7558.3656 


308 . 1902 




8 


7208 . 1016 


300.9646 


2 


7573.7830 


308.5044 




9 


7223.1577 


301.2787 


3 


7589. 2161 


308.8186 


96 





7238.2295 


301.5929 


4 


7604.6648 


309.1327 




I 


7253.3170 


301.9071 


5 


7620.1293 


309.4469 




2 


7268.4202 


302 . 2212 


6 


7635.609s 


309.7610 




3 


7283.5391 


302.5354 


7 


7651 . 1054 


310.0752 




4 


7298.6737 


302.8405 


8 


7666.6170 


310.3894 




S 


7313.8240 


303.1637 


9 


7682.1444 


310.7035 




6 


7328.9901 


303.4779 99 





7697.6893 


31 I. 0177 




1 


7344. 1718 


303.7920 


I 


7713. 2461 


31 I. 3318 




8 


7359.3693 


304.1062 


2 


7728.8206 


■ 311.6460 




9 


7374-5824 


304.4203 


3 


7744.4107 


311.9602 


97 





7389. 8113 


304.7345 • 


4 


7760.0166 


312.2743 




I 


7405.0559 


305.0486 


5 


7775.6382 


312. 588s 




2 


7420.3162 


305.3628 


6 


7791-2764 


312.9026 




3 


7435.5922 


305.6770 


7 


7806.9284 


313.2168 




4 


7450.8839 


305.9911 


8 


7822.5971 


313.5309 




5 


7466. 1913 


306.3053 


9 


7838. 281S 


313.8451 




6 


7481 . 5144 


306.6194 100 





7853.9816 


314.1593 




7 


7496.8532 


306.9336 









To compute the area or circumference of a circle of a diameter greater than 
100 and less than looi; 

Take out the area or circumference from table as though the number 
had one decimal, and move the decimal point two places to the right for 
the area, and one place for the circumference. 

Example. — Wanted the area and circumference of 567. The tabular 
area for 56.7 is 2524.9687, and circumference 178.1283. Therefore area 
for 567 = 252496.87 and circumference = 1781.283. 

To compute the area or circumference of a circle of a diameter greater than 
1000, 

Divide by a factor, as 2, 3, 4, 5, etc., if practicable, that will leave a 
quotient to be found in table, then multiply the tabular area of the 
quotient by the square of the factor, or the tabular circumference by the 
factor. 

Example. — Wanted the area and circumference of 2109, Dividing 
by 3, the quotient is 703, for which the area is 388150.84 and the circum- 
ference 2208.54. Therefore area of 2109 = 388150.84 X 9 = 3493357-56 
and circumference = 2208.54 X 3 = 6625.62. 



So 



Mathematical Tables 



Table of Circular Arcs 

Length of circular arcs when the chord and the height of the arc are given. 

Divide the height by the chord. Find in the column of Heights the number 
equal to this quotient. 

Take out the corresponding number from the column of lengths. 
Multiply this last number by the length of the given chord. 



Heights 


Lengths 


Heights 


Lengths 


Heights 


Lengths 


Heights 


Lengths 


.001 


1.00002 


.049 


1.00638 


.097 


I. 02491 


.145 


I. 05516 


.002 


1.00002 


.050 


1.00665 


.098 


1.02542 


.146 


I -05591 


.003 


1.00003 


.051 


1.00692 


•099 


1.02593 


• 147 


1.05667 


.004 


1.00004 


.052 


1.00720 


.100 


1.02646 


.148 


1.05743 


.005 


1.00007 


.CS3 


1.00748 


.101 


1.02698 


-149 


I. 05819 


.006 


I.OOOIO 


•OS4 


I .00776 


.102 


1.02752 


.150 


1.05896 


.007 


I. 00013 


.055 


1.00805 


.103 


1.02806 


■ 151 


I OS973 


.008 


I. 00017 


.056 


1.00834 


.104 


1.02860 


.152 


I. 06051 


.009 


1.00022 


.057 


1.00864 


.105 


I. 02914 


• 153 


I. 06130 


.010 


1.00027 


.058 


1.00895 


.106 


1.02970 


-154 


1.06209 


.011 


1.00032 


.059 


1.00926 


.107 


1.03026 


• 155 


1.06288 


.012 


1.00038 


.060 


1.00957 


.108 


1.03082 


.156 


1.06368 


.013 


1.00045 


.061 


1.00989 


.109 


I 03139 


• 157 


1.06449 


.014 


1.00053 


.062 


1.01021 


.110 


I. 03196 


.158 


1.06530 


•ois 


I. 00061 


.063 


I. 01054 


.III 


1.03254 


■159 


1.06611 


.016 


1.00069 


.064 


I. 01088 


.112 


I. 03312 


.160 


1.06693 


.017 


1.00078 


.065 


1.01123 


-113 


I 03371 


.161 


1.0677s 


.018 


1.00087 


.066 


I. 01 158 


.114 


I 03430 


.162 


1.06858 


.019 


1.00097 


.067 


I. 01 193 


• 115 


1.03490 


.163 


I. 06941 


.020 


I. 00107 


.068 


I. 01228 


.116 


I. 03551 


.164 


1.07025 


.021 


1.00117 


.069 


I. 01264 


.117 


I. 0361 I 


.16s 


I. 07109 


.022 


I. 00128 


.070 


I. 01302 


.iiS 


1.03672 


.166 


I. 07194 


.023 


I. 00140 


.071 


I. 01338 


.119 


1.03734 


.167 


1.07279 


.024 


I. 00153 


.072 


I. 01376 


.120 


1-03797 


.168 


1.07365 


.025 


I. 00167 


.073 


1.01414 


.121 


1.03860 


.169 


I. 07451 


.026 


I. 00182 


.074 


I -01453 


.122 


1.03923 


.170 


I.07S37 


.027 


I. 00196 


.075 


I. 01493 


.123 


1.03987 


.171 


1.07624 


.028 


I. 002 10 


.076 


I -01533 


.124 


I. 04051 


.172 


I.077H 


.029 


1.00225 


.077 


I -01573 


.125 


I. 041 16 


.173 


1.07799 


.030 


I .00240 


.078 


1.01614 


.126 


1.04181 


.174 


1.07888 


.031 


1.00256 


.079 


I. 01656 


.127 


1.04247 


.175 


1.07977 


.032 


1.00272 


.080 


I. 01698 


.128 


1.04313 


.176 


1.08066 


.033 


1.00289 


.081 


1.01741 


.129 


1.04380 


.177 


I. 08156 


-034 


1.00307 


.082 


I. 01784 


.130 


1.04447 


.178 


1.08246 


.035 


1.00327 


.083 


I. 01828 


.131 


I. 04515 


■ .179 


1.08337 


.036 


I.C034S 


.0S4 


I. 01872 


.132 


1.04584 


.180 


1.08428 


.037 


1.00364 


.085 


1.01916 


• 133 


1.04652 


.181 


I. 08519 


.038 


1.00384 


.086 


1.01961 


.134 


I .04722 


.182 


1.08611 


.039 


1.00405 


.087 


I .02006 


• 135 


I .04792 


.183 


1.08704 


.040 


1.00426 


.088 


1.02052 


.136 


1.04862 


.184 


1.08797 


.041 


1.00447 


.089 


1.02098 


• 137 


1.04932 


.185 


1.08890 


.042 


I .00469 


.090 


I. 02146 


.138 


1.05003 


.186 


1.08984 


•043 


1.00492 


.091 


I .02192 


.139 


1.05075 


.187 


1.09079 


.044 


I. 00515 


.092 


1.02240 


.140 


I. 05147 


.188 


I. 09174 


.045 


I.C50539 


.093 


1.02CS9 


.141 


1.05220 


.189 


1.09269 


.046 


1.00563 


.094 


1.02339 


.142 


1.05293 


.190 


1.0936s 


.047 


1.00587 


.095 


1.02389 


.143 


1.05367 


.191 


I. 09461 


.048 


I. 00612 


.096 


1.02440 


.144 


I. 05441 


.192 


I.09SS7 



Table of Circular Arcs 
Table of Circular Arcs — (Contimied) 



8i 



Heights 


Lengths 


Heights 


Lengths He 


ights 


Lengths He 


ights L 


engths 


.193 


1.09654 


.248 


I. 15670 


303 


1.22920 


358 I 


31276 


.194 


1.09752 


.249 


1.15791 


304 


1.23063 


359 I 


31437 


.195 


1.09850 


.250 


1.15912 


30s 


I . 23206 


360 I 


31599 


.196 


1.09949 


.251 


I. 16034 


306 


1.23349 


361 I 


31761 


.197 


I . 10048 


.252 


1.16156 


307 


1.23492 


362 I 


31923 


.198 


1 . 10147 


.253 


I. 16279 


308 


1.23636 


363 I 


32086 


• 199 


1. 10247 


.254 


I . 16402 


309 


I. 23781 


364 I 


32249 


.200 


I. 10347 


.255 


I . 16526 


310 


1.23926 


365 I 


32413 


.201 


I. 10447 


.256 


I . 16650 


311 


1.24070 


366 I 


32577 


.202 


I. 10548 


.257 


I . 16774 


312 


I. 24216 


357 I 


32741 


.203 


I. 10650 


.258 


I. 16899 


313 


I. 24361 


368 I 


3290s 


.204 


I.I07S2 


.259 


I . 17024 


314 


1.24507 


369 I 


33069 


.205 


I. 10855 


.260 


I . 17150 


315 


1.24654 


370 I 


33234 


.206 


I . 10958 


.261 


I. 17276 


316 


I . 24801 


371 I 


33399 


.207 


I.11062 


.262 


1.17403 


317 


1.24948 


372 I 


33564 


.208 


1.1116s 


.263 


I. 17530 


318 


1.25095 


373 I 


33730 


.209 


1.11269 


.264 


I . 17657 


319 


1.25243 


374 I 


33896 


.210 


I.11374 


.265 


I . 17784 


320 


I. 25391 


375 I 


34063 


.211 


I.I1479 


.266 


1.17912 


321 


1.25540 


376 I 


34229 


.212 


1.11S84 


.267 


I . 18040 


322 


1.25689 


377 I 


34396 


.213 


1.11690 


.268 


I . 18169 


323 


1.25838 


378 I 


34563 


.214 


1.I1796 


.269 


I . 18299 


324 


1.25988 


379 I 


34731 


.215 


I. I 1904 


.270 


I. 18429 


325 


I. 26138 


380 I 


34899 


.216 


1.12011 


.271 


I . 18559 


326 


1.26288 


381 I 


35068 


.217 


1.12118 


.272 


I. 18689 


327 


1.26437 


382 I 


35237 


.218 


I . 12225 


.273 


I . 18820 


328 


1.26588 


383 I 


35406 


.219 


I. 12334 


.274 


1.18951 


329 


I . 26740 


384 I 


35575 


.220 


I . 12444 


.275 


I. 19082 


330 


1.26892 


385 I 


35744 


.221 


I. 12554 


.276 


1.19214 


331 


1.27044 


386 I 


35914 


.222 


I. 12664 


.277 


I. 19346 


332 


1.27196 


387 I 


36084 


.223 


I. 12774 


.278 


I. 19479 


333 


1.27349 


388 I 


36254 


.224 


1.1288s 


.279 


1.19612 


334 


1.^502 


389 I 


36425 


.225 


I. 12997 


.280 


I . 19746 


335 


1.27656 


390 I 


36596 


.226 


I . 13108 


.281 


I . 19880 


336 


I. 27810 


391 I 


36767 


.227 


I . 13219 


.282 


I. 20014 


337 


1.27964 


392 I 


36939 


.228 


I.13331 


.283 


I. 20149 


338 


1.28118 


393 I 


37111 


.229 


I. 13444 


.284 


1.20284 


339 


1.28273 


394 I 


37283 


.230 


I. 13557 


.28s 


I . 20419 


340 


1.28428 


395 I 


37455 


.231 


1.13671 


.286 


I.20S5S 


341 


1.28583 


396 I 


37628 


.232 


I. 13785 


.287 


I. 20691 


342 


1.28739 


397 I 


37801 


.233 


I. 13900 


.288 


1.20827 


343 


1.28895 


398 I 


37974 


.234 


I-I4015 


.279 


1.20964 


344 


1.29052 


399 I 


38148 


.235 


I.14131 


.290 


I. 21 102 


345 


1.29209 


400 I 


.38322 


.236 


I. 14247 


.291 


I. 21239 


346 


1.29366 


401 I 


38496 


.237 


I. 14363 


.292 


I. 21377 


347 


1.29523 


402 I 


38671 


.238 


I. 14480 


.293 


1.21515 


348 


I. 29681 


403 I 


38846 


.239 


I. 14597 


.294 


1.21654- 


349 


1.29839 


404 I 


39021 


.240 


I.14714 


.295 


I. 21794 


350 


1.29997 


405 I 


39196 


.241 


I. 14832 


.296 


I. 21933 


351 


1.30156 


406 I 


39372 


.242 


I . 14951 


.297 


1.22073 


352 


1.3031S 


407 I 


.39548 


.243 


I . 15070 


.298 


I. 22213 


.353 


1.30474 


408 I 


39724 


.244 


1.IS189 


.299 


1.22354 


.354 


1.30634 


409 I 


39900 


.245 


I . 15308 


.300 


1.22495 


.355 


1.30794 


410 I 


.40077 


.246 


I. 15428 


.301 


1.22636 


.356 


1.30954 


411 I 


40254 


.247 


I . 15549 


.302 


1.22778 


.357 


I.3111S 


.412 I 


.40432 



82 



Mathematical Tables 
Table of Circular Arcs — {Concluded) 



Heights 


Lengths 


Heights 


Lengths 


Heights 


Lengths He 


ights 


Lengths 


.413 


1. 40610 


.435 


1.44589 


.457 


1.48699 


479 


1.52931 


.414 




40788 


.436 




44773 


.458 


1.48889 


480 


1. 53126 


.415 




40966 


.437 




44957 


.459 


1.49079 


481 


1.53322 


.416 




41145 


.438 




45142 


.460 


1.49269 


482 


I. 53518 


.417 




41324 


.439 




45327 


.461 


1.49460 


483 


I. 53714 


.418 




41503 


.440 




45512 


.462 


I. 49651 


484 


I. 53910 


.419 




41682 


.441 




45697 


.463 


1.49842 


485 


I . 54106 


.420 




41861 


.442 




45883 


.464 


1.50033 


486 


1.54302 


.421 




42041 


.443 




46069 


.465 


1.50224 


487 


1.54499 


.422 




42221 


-.444 




46255 


.466 


I. 50416 


488 


1.54696 


.423 




42402 


.445 




46441 


.467 


1.50608 


489 


1.54893 


.424 




42583 


.446 




46628 


.468 


1.50800 


490 


I. 55091 


.42s 




42764 


.447 




46815 


.469 


1.50992 


491 


1.55289 


.426 




42945 


.448 


•'• 


47002 


.470 


1.51185 


492 


1.55487 


.427 




43127 


.449 




47189 


.471 


I. 51378 


493 


1.5568s 


.428 




43309 


.450 




47377 


.472 


1.51571 


494 


1.55884 


.429 




43491 


.451 




4756s 


.473 


I. 51764 


495 


1.56083 


.430 




43673 


.452 




47753 


.474 


I. 51958 


496 


1.56282 


.431 




43856 


.453 




47942 


.475 


I. 52152 


497 


1.56481 


.432 




44039 


.454 




48131 


.476 


1.52346 


498 


1.56681 


.433 




44222 


.455 




48320 


.477 


I. 52541 


499 


I. 56881 


.434 




44405 


.456 




48509 


.478 


1.52736 


500 


1.57080 



Lengths of Circular Arcs to Radius 1 

To find the length of a circular arc by the following table 

Knowing the radius of the circle and the measure of the arc in deg., 
min., etc. 

Rule. — Add together the lengths in the table found respectively 
opposite to the deg., min., etc., of the arc. Multiply the sum by the 
radius of the circle. 

Example. — In a circle of 12.43 f^et radius, is an arc of 13 deg., 27 min., 
8 sec. How long is the arc? 

Here, opposite 13 deg. in the table, we find .2268928 

" 27 min. " " " " .0078540 
" • 8 sec. " " " " .0000388 



Sum =.2347856 

And .2347856 X 12.43, or radius = 2.918385 feet, the required length 
of arc. 



Lengths of Circular Arcs to Radius i 83 

Lengths of Circular Arcs to Radius i 



Deg. 


Length 


Deg. 


Length 


Deg. 


Length 


Deg. 
136 


Length 


I 


.0174533 


46 


.8028515 


91 


1.5882496 


2.3736478 


2 


.0349066 


47 


.8203047 


92 


1.6057029 


137 


2. 391 ion 


3 


.0523599 


48 


.8377580 


93 


I. 6231562 


138 


2.4085544 


4 


.0698132 


49 


.8552113 


94 


I . 6406095 


139 


2 . 4260077 


5 


087266s 


50 


.8726646 


95 


1.6580628 


140 


2.4434610 


6 


.1047198 


SI 


.8901179 


96 


1.6755161 


141 


2 . 4609142 


7 


.1221730 


52 


.9075712 


97 


1.6929694 


142 


2.4783675 


8 


.1396263 


53 


.9250245 


98 


I. 7104227 


143 


2.4958208 


9 


.1570796 


54 


.9424778 


99 


I . 7278760 


144 


2.5132741 


10 


.1745329 


55 


.9593911 


100 


1.7453293 


145 


2.5307274 


II 


. 1919862 


56 


.9773844 


lOI 


1.762782s 


146 


2.5481807 


12 


.2094395 


57 


.9948377 


102 


1.7802358 


147 


2.5656340 


13 


.2268928 


58 


1.0122910 


103 


I. 7976891 


148 


2.5830873 


14 


.2443461 


59 


1.0297443 


104 


1.8151424 


149 


2.6005406 


IS 


.2617994 


60 


I. 047 1976 


105 


1.8325957 


150 


2.6179939 


16 


. 2792527 


61 


1.0646508 


106 


1.8500490 


151 


2.6354472 


17 


. 2967060 


62 


1.0821041 


107 


1.8675023 


152 


2.6529005 


18 


.3141593 


63 


1.0995574 


108 


1.8849556 


153 


2.6703538 


19 


.3316126 


64 


I . 1170107 


109 


1.9024089 


154 


2.6878070 


20 


.3490659 


65 


I. 1344640 


no 


I. 9198622 


I5S 


2.7052603 


21 


.3665191 


66 


1.1519173 


III 


I. 9373155 


156 


2.7227136 


22 


.3839724 


67 


I . 1693706 


112 


1.9547688 


157 


2 . 7401669 


23 


.4014257 


68 


I . X868239 


113 


1,9722221 


158 


2 . 7576202 


24 


.4188790 


69 


1.2042772 


114 


1.9896753 


159 


2.7750735 


25 


.4363323 


70 


I. 2217305 


115 


2.0071286 


160 


2.7925268 


26 


.4537856 


71 


I. 2391838 


116 


2.0245819 


161 


2 . 8099801 


27 


.4712389 


72 


I. 2566371 


117 


2.0420352 


162 


2.8274334 


28 


.4886922 


73 


1.2740904 


118 


2.0594885 


163 


2 . 8448867 


29 


.5061455 


74 


I. 2915436 


119 


2.0769418 


164 


2.8623400 


30 


.5235988 


75 


1.3089969 


120 


2.0943951 


165 


2.8797933 


31 


.5410521 


76 


1.3264502 


121 


2. I I 18484 


166 


2.8972466 


32 


.5585054 


77 


1.343903s 


122 


2.1293017 


167 


2.9146999 


33 


.5759587 


78 


I. 3613568 


123 


2 . 1467550 


168 


2.9321531 


34 


.5934119 


79 


1.3788101 


124 


2 . 1642083 


169 


2.9496064 


35 


.6108652 


80 


1.3962634 


125 


2.1816616 


170 


2.9670597 


36 


.6283185 


81 


1.4137167 


126 


2.1991149 


171 


2.9845130 


37 


.6457718 


82 


1.4311700 


127 


2.2165682 


172 


3.0019663 


38 


.6632251 


83 


1.4486233 


128 


2.2340214 


173 


3.0194x96 


39 


.6806784 


84 


1.4660766 


129 


2.2514747 


174 


3.0368729 


40 


.6981317 


. 85 


1.4835299 


130 


2.2689280 


175 


3.0543262 


41 


.7155850 


86 


1.5009832 


131 


2.2863813 


176 


3.0717795 


42 


.7330383 


87 


I. 5184364 


132 


2.3038346 


177 


3.0892328 


43 


.7504916 


88 


1.5358897 


133 


2.3212879 


178 


3.1066861 


44 


.7679449 


89 


I • 5533430 


134 


2.3387412 


179 


3.1241394 


45 


.7853982 


90 


1.5707963 


135 


2.3561945 


180 


3.1415927 



Min. 


Length 


Min. 


Length 


Min. 


Length 


Min. 


Length 


I 


.0002909 


6 


.OOI74S3 


II 


.0031998 


16 


.0046542 


2 


.0005818 


7 


.0020362 


12 


.0034907 


17 


.0049451 


3 


.0008727 


8 


.0023271 


13 


.0037815 


18 


.0052360 


4 


.0011636 


9 


.0026180 


14 


.0040724 


19 


.0055269 


5 


.0014544 


10 


.0029089 


15 


.0043633 


20 


.0058178 



84 Mathematical Tables 

Lengths or Circular Aecs to Radius i — {Continued) 



Min. 


Length 


Min. 


Length 


Min. 


Length 


Min. 


Length 


21 


.0061087 


31 


.0090175 


• 
41 


.0119264 


SI 


0148353 


22 


.0063995 


32 


.0093084 


42 


.0122173 


52 


.0151262 


23 


.0066904 


33 


.0095993 


43 


.0125082 


53 


.0154171 


24 


.0069813 


34 


.0098902 


44 


.0127991 


54 


0157080 


25 


.0072722 


35 


.0101811 


45 


.0130900 


55 


.0159989 


26 


.0075631 


36 


.0104720 


46 


.0133809 


56 


.0162897 


27 


.0078540 


37 


.0107629 


47 


.0136717 


57 


.0165806 


28 


.00S1449 


38 


.0110538 


48 


.0139626 


58 


.0168715 


29 


.0084358 


39 


.0113446 


49 


.0142535 


59 


.0171624 


30 


.oc^7266 


40 


.0116355 


50 


.0145444 

1 


60 


.0174533 



Sec. 


Length 


Sec. 


Length 


Sec. 


Length 


Sec. 


Length 


I 


.0000048 


16 


.0000776 


31 


.0001503 


46 


.0002230 


2 


0000097 


17 


.0000824 


32 


.0001551 


47 


.0002279 


3 


.0000145 


18 


.0000873 


33 


.0001600 


48 


.0002327 


4 


.0000194 


19 


.0000921 


34 


.0001648 


49 


.0002376 


5 


0000242 


20 


.0000970 


35 


.0001697 


50 


.0002424 


6 


0000291 


21 


.0001018 


36 


.0001745 


51 


.0002473 


7 


0000339 


22 


.0001067 


37 


.0001794 


52 


.0002521 


8 


0000388 


23 


.0001115 


38 


.0001842 


53 


.0002570 


9 


0000430 


24 


.0001164 


39 


.0001891 


54 


.0002618 


10 


0000485 


25 


.0001212 


40 


.0001939 


55 


.0002666 


II 


0000533 


26 


.0001261 


41 


.0001988 


56 


.0002715 


12 


0000582 


27 


.0001309 


42 


.0002036 


. 57 


.0002763 


13 


0000630 


28 


.0001357 


43 


.0002085 


58 


.0002812 


14 


0000679 


29 


.0001406 


44 


.0002133 


59 


.0002860 


15 


0000727 


30 


.0001454 


45 


.0002182 

1 


60 


.0002909 



Table of Areas of Circular Segments 

If the segment exceeds a semicircle, its area = area of circle — area of a segment 
whose rise = (diam. of circle — rise of given segment). Diam. of circle = (square 
of half chord -^ rise) + rise, whether the segment exceeds a semicircle or not. 



Rise 
divided 
by diam. 


Area = 

(square 

of diam.) 

multi- 


Rise 
divided 
by diam. 


Area = 

(square 

of diam.) 

multi- 


Rise 
divided 
by diam. 


Area = 

(square 

of diam.) 

multi- 


Rise 
divided 
by diam. 


Area = 

(square 

of diam.) 


of circle 


plied by 


of circle 


plied by 


of circle 


plied by 


of circle 


plied by 


.001 


.000042 


.010 


.001329 


.019 


.003472 


.028 


.006194 


.002 


.000119 


.011 


.001533 


.020 


.003749 


.029 


.006527 


.003 


.000219 


.012 


.001746 


.021 


.004032 


.030 


.006866 


.004 


.000337 


.013 


.001969 


.022 


.004322 


.031 


.007209 


.005 


.000471 


.014 


.002199 


.023 


.004619 


.032 


.007559 


.006 


.000619 


.015 


.002438 


.024 


.004922 


.033 


.007913 


.007 


.000779 


.016 


.002685 


.025 


.005231 


.034 


.008273 


.008 


.000952 


.017 


.002940 


.026 


.005546 


.035 


.008638 


.009 


.001135 


.018 


.003202 


.027 


.005867 


.036 


.009008 



Table of Areas of Circular Segments 



8s 





Table of 


Areas of Circular Segments — 


{Continued) 


Rise 
divided 
by diam. 


Area = 

(square 

of diam.) 


Rise 
divided 
by diam. 


Area = 

(square 

of diam.) 

multi- 


_ . Area = 

^^}f^ (square 
divided ^f^i^^_) 

by diam. ^^j^.. 


Rise 
divided 
by diam. 


Area= 

(square 

of diam.) 

multi- 


of circle 


plied by 


of circle 


plied by 


°f"^^^« plied by 


of circle 


plied by 


.037 


.009383 


.087 


.033308 


.137 


.064761 


.187 


. IOISS3 




.038 


.009764 


.088 


.033873 


.138 


.065449 


.188 


■ 102334 




.039 


.010148 


.089 


.034441 


.139 


.066140 


.189 


• 103116 




.040 


.010538 


.090 


.035012 


.140 


.066833 


.190 


.103900 




.041 


.010932 


.091 


.035586 


.141 


067528 


.191 


. 104686 




.042 


.011331 


.092 


.036162 


,142 


068225 


.192 


. 105472 




•043 


.011734 


.093 


.036742 


.143 


068924 


.193 


. 106261 




.044 


.012142 


.094 


•037324 


.144 


069626 


.194 


. 107051 




04s 


.012555 


.095 


.037909 


.145 


070329 


• 195 


.X07843 




.046 


.012971 


.096 


, .038497 


.146 


071034 


.196 


.108636 




.047 


.013393 


.097 


.039087 


• 147 


071741 


.197 


-109431 




.048 


.013818 


.098 


.039681 


.148 


072450 


.198 


. 110227 




.049 


.014248 


.099 


.040277 


.149 


073162 


.199 


. 111025 




.oso 


.014681 


.100 


.040875 


.ISO 


073875 


.200 


. 111824 




.051 


.015119 


.101 


.041477 


.151 


074590 


.201 


.112625 




.052 


.015561 


.102 


.042081 


.152 


075307 


.202 


.113427 




053 


.016008 


.103 


.042687 


.153 


076026 


.203 


.114231 




OS4 


.016458 


.104 


.043296 


.154 


076747 


.204 


.115036 




055 


.016912 


.105 


.043908 


.155 


077470 


.205 


.115842 




056 


.017369 


.106 


•044523 


.156 


078194 


.206 


.116651 




057 


.017831 


.107 


.045140 


.157 


078921 


.207 


.117460 




058 


.018297 


.108 


•0457S9 


.158 


079650 


.208 


.118271 




059 


.018766 


.109 


.046381 


.159 


080380 


.209 


.119084 




060 


.019239 


.110 


.047006 


.160 


081 I 12 


.210 


.119898 




061 


.019716 


.III 


•047633 


.161 


081847 


.211 


.120713 




062 


.020197 


.112 


.048262 


.162 


082582 


.212 


•121530 




063 


.020681 


.113 


.048894 


.163 


083320 


.213 


.122348 




064 


.021168 


.114 


.049529 


.164 


084060 


.214 


.r23i67 




065 


.021660 


.115 


.050165 


.165 


084801 


.215 


.123988 




066 


.022155 


.116 


.050805 


.166 


085545 


.216 


. 124811 




067 


.0236S3 


.117 


.051446 


.167 


086290 


.217 


•125634 




068 


.023155 


.118 


.052090 


.168 


087037 


.218 


. 126459 




069 


.023660 


.119 


.052737 


.169 


087785 


.219 


. 127286 




070 


.024168 


.120 


•053385 


.170 


088536 


.220 


.128114 




071 


.024680 


.121 


•054037 


.171 


089288 


.221 


.128943 




072 


.025196 


.122 


.054690 


.172 


090042 


.222 


.129773 




073 


.025714 


.123 


•055346 


.173 


090797 


.223 


.13060S 




074 


.026236 


.124 


.056004 


.174 


091555 


.224 


.131438 




075 


.026761 


.125 


.056664 


.175 


092314 


.225 


.132273 




076 


.027290 


.126 


.057327 


.176 


093074 


.226 


.133109 




077 


.027821 


.127 


•057991 


.177 


093837 


.227 


.133946 




078 


.028356 


.128 


.058658 


.178 


094601 


.228 


.134784 




079 


.028894 


.129 


.059328 


.179 


095367 


.229 


.135624 




080 


.029435 


-.130 


■059999 


.180 


096135 


.230 


.13646S 




081 


.029979 


.131 


.060673 


.181 


096904 


.231 


.137307 




082 


.030526 


.132 


.061349 


.182 


097675 


.232 


.138151 




083 


.031077 


.133 


.062027 


.183 


098447 


.233 


.138996 




084 


.031630 


.134 


.062707 


.184 


099221 


.234 


.139842 




085 


.032186 


.1.35 


.063389 


.185 


099997 


.235 


.140689 


!o86 


.032746 


.136 


.064074 


.186 


100774 


.236 


.141538 



S6 



Mathematical Tables 



Table of 


Areas 


DF Circular Segments — 


(Continued) 


Rise 
divided 
by diam. 


Area = 

(square 

of diam.) 

multi- 


Rise 
divided 
by diam. 


Area = 

(square 

of diam.) 

multi- 


Rise 
divided 
by diam. 


Area = 
(square 
of diam.) 
multi- 


Rise 
divided 
by diam. 


Area = 

(square 

of diam.) 

multi- 


of circle 


plied by 


of circle 


plied by 


of circle 


plied by 


of circle 


pUed by 


.237 


.142388 


.287 


. 186329 


.337 


.232634 


.387 


.280669 


.238 


.143239 


.288 


. 187235 


.338 


.233580 


.388 


.281643 


.239 


. 144091 


.289 


. 188141 


.339 


.234526 


.389 


.282618 


..240 


.144945 


.290 


.189048 


.340 


.235473 


.390 


.283593 


.241 


.145800 


.291 


.189956 


.341 


.236421 


.391 


.284569 


.242 


.146656 


.292 


.190865 


.342 


.237369 


.392 


.285545 


.243 


.147513 


.293 


.191774 


.343 


.238319 


.393 


.286521 


.244 


.148371 


.294 


. 192685 


.344 


.239268 


.394 


.287499 


.245 


.149231 


.295 


.193597 


.345 


.240219 


.395 


.288476 


.246 


.150091 


.296 


.194509 


.346 


.241170 


.396 


.289454 


.247 


.150953 


.297 


.195423 


.347 


.242122 


.397 


.290432 


.248 


.151816 


.298 


.196337 


.348 


.243074 


.398 


.291411 


.249 


. 152681 


.299 


.197252 


.349 


.244027 


-399 


.292390 


.250 


.153546 


.300 


.198168 


.350 


.244980 


.400 


.293370 


.251 


.154413 


.301 


.199085 


.351 


.245935 


.401 


.294350 


.252 


.155281 


.302 


.200003 


.352 


.246890 


.402 


.295330 


.253 


.156149 


.303 


.200922 


.353 


.247845 


.403 


.296311 


.254 


.157019 


.304 


. 201841 


.354 


.248801 


.404 


.297292 


.255 


.157891 


.305 


.202762 


.355 


.249758 


.40s 


.298274 


.256 


.158763 


.306 


.203683 


.356 


.250715 


.406 


.299256 


.257 


.159636 


.307 


. 204605 


.357 


.251673 


.407 


.300238 


.258 


.160511 


.308 


. 205528 


.358 


.252632 


.408 


.301221 


.259 


.161386 


.309 


.206452 


.359 


.253591 


.409 


.302204 


.260 


. 162263 


.310 


.207376 


.360 


.254551 


.410 


.303187 


.261 


. 163141 


.311 


.208302 


.361 


.255511 


.411 


.304171 


.262 


. 164026 


.312 


.209228 


.362 


.256472 


.412 


.305156 


.263 


.164900 


.313 


.2IOI5S 


.363 


.257433 


.413 


.306140 


.264 


.165781 


.314 


.211083 


.364 


.258395 


.414 


.307125 


.26s 


.166663 


.315 


.212011 


.365 


.259358 


.415 


.308110 


.266 


.167546 


.316 


.212941 


.366 


.260321 


.416 


.309096 


.267 


.168431 


.317 


.213871 


.367 


.261285 


.417 


.310082 


.268 


. 169316 


.318 


. 214802 


.368 


.262249 


.418 


.311068 


.269 


.170202 


.319 


.215734 


.369 


.263214 


.419 


.312055 


.270 


.171090 


.320 


.216666 


.370 


.264179 


.420 


.313042 


.271 


.171978 


.321 


.217600 


.371 


.265145 


.421 


.314029 


.272 


.172868 


.322 


.218534 


.372 


.266111 


.422 


.315017 


.273 


.173758 


.323 


.219469 


.373 


.267078 


.423 


.316005 


.274 


. 174650 


.324 


.220404 


.374 


.268046 


.424 


.316993 


.275 


.175542 


.325 


.221341 


.375 


.269014 


.425 


.317981 


.276 


. 176436 


.326 


. 222278 


.376 


.269982 


.426 


.318970 


.277 


.177330 


.327 


.223216 


.377 


.270951 


.427 


.319959 


.278 


.178226 


.328 


.224154 


.378 


.271921 


.428 


.320949 


.279 


.179122 


.329 


.225094 


.379 


.272891 


.429 


.321938 


.280 


.180020 


.330 


.226034 


.380 


.273861 


.430 


.322928 


.281 


. 180918 


.331 


.226974 


.381 


.274832 


.431 


.323919 


.282 


.181818 


.332 


.227916 


.382 


.275804 


.432 


.324909 


.283 


. 182718 


.333 


.228858 


.383 


.276776 


.433 


.325900 


.284 


. 183619 


.334 


.229801 


.384 


.277748 


.434 


.326891 


.285 


. 184522 


.335 


.230745 


.385 


.278721 


.435 


.327883 


.286 


.185425 


.336 


.231689 


.386 


.279695 


.436 


.328874 



Table of Areas of Circular Segments 



87 



Table of' Areas of Circular Segments — {Continued) 



Rise 
divided 


Area = 
(square 


Rise 
divided 


Area= j 
(square ^^ 


lise 
^ided 


Area = j 
(square ^j, 


Use 

/ided 


Area = 
(square 


by diam. 
of circle 


of diam.) 
multi- 


by diam. 
of circle 


of diam.) , 
multi- J 


diam. 
circle 


of diam.) , 
multi- q£ 


diam. 
circle 


of diam.) 
multi- 




plied by 




plied by 




plied by 




plied by 


.437 


.329866 


.453 


.345768 


.469 


.361719 


485 


.377701 


.438 


.330858 


.454 


.346764 


470 


.362717 


486 


.378701 


.439 


.331851 


.455 


.347760 


471 


.363715 


487 


.379701 


.440 


.332843 


.456 


.348756 


472 


.364714 


488 


.380700 


.441 


.333836 


.457 


.349752 


473 


.365712 


489 


.381700 


.442 


.334829 


.458 


.350749 


474 


.366711 


490 


.382700 


.443 


.335823 


.459 


.351745 


475 


.367710 


491 


.383700 


• .444 


.336816 


.460 


.352742 


476 


.368708 


492 


.384699 


-445 


.337810 


.461 


.353739 


477 


.369707 


493 


.385699 


.446 


.338804 


.462 


.354736 


478 


.370706 


494 


.386699 


.447 


.339799 


.463 


.355733 


479 


.371705 


495 


.387699 


.448 


.340793 


.464 


.356730 


480 


.372704 


496 


.388699 


.449 


.341788 


.465 


.357728 


481 


.373704 


497 


.389699 


.450 


.342783 


.466 


.358725 


482 


.374703 


498 


.390699 


.451 


.343778 


.467 


.359723 


483 


.375702 


499 


.391699 


.452 


.344773 


.468 


.360721 


484 


.376702 


500 


.392699 



88 



Mathematical Tables 



Chords of Arcs from One to Ninety Degrees 

Dimensions given in inches. 



Ang. 


18-inch 


36-inch 


72-inch 


Ang. 
Deg. 


18-inch 


36-inch 


72-inch 


radius 


radius 


radius 


radius 


radius 


radius 


Deg. 


chord 


chord 


chord 


chftrd 


chord 


chord 


I 


Vi6 


% 


iH 


46 


14 1/1 6 


281/i 


561/64 


2 


^A 


iV^ 


2/2 


47 


1423/64 


2823/32 


572/64 


3 


1^6 


m 


33/4 


48 


14^/64 


29%2 


583/64 


4 


iH 


2V, 


5 


49 


145 %4 


2955/4 


5923/2 


5 


l3%4 


3%4 


6?^2 


50 


I5%2 


302 %4 


6055/64 


6 


lli 


34 %4 


7I/32 


51 


15/2 


31 


62 


7 


21^64 


42"5/64 


851/^4 


52 


1525/32 


319/6 


63% 


8 


2H 


5/64 


IO%4 


53 


16/16 


32% 


641/4 


9 


253/^4 


5^/64 


Ill%4 


54 


16I/32 


321/6 


653/ 


lO 


39/64 


6^32 


123 %4 


55 


l65/^ 


33/ 


66/2 


II 


32 9/64 


62 9/32 


135/64 


56 


162 9/32 


33^/64 


6739/4 


12 


34 %4 


71/32 


IS%4 


57 


I7IH4 


3423/64 


6823/2 


13 


4^/64 


8/32 


l61%4 


58 


172/64 


3429/2 


6913/6 


14 


42 %4 


825/32 


1735/64 


59 


1723/32 


3529/4 


7029/2 


15 


4^5/64 


925/64 


1851/64 


60 


18 


36 


72 


i6 


5 


10^4 


20H2 


61 


181/64 


3635/4 


735/64 


17 


521/64 


104^4 


21%2 


62 


1835/64 


37/64 


74II/64 


i8 


SH 


Ill%4 


22l%2 


63 


181 /l 6 


37% 


7514 


19 


5^5/16 


11% 


234%4 


64 


19/64 


385/2 


765/6 


20 


6I/4 


12/2 


25 


65 


I9IH2 


38II/16 


7734 


21 


6^16 


T-zY^ 


2615/64 


66 


1939/64 


39%2 


782 %4 


22 


674 


134 %4 


273/64 


67 


19% 


39^/64 


7915/2 


23 


7"/64 


142/64 


28* %4 


68 


2ol,i 


4oi%4 


8oi%2 


24 


73/64 


143/32 


291 5/6 


69 


2o2 5/^4 


4o2%2 


8x9/6 


25 


7^/64 


153/64 


311/64 


70 


20*1/64 


4ii%4 


82l%2 


26 


83/^2 


161^^4 


3225/64 


71 


2o2%2 


4I13/6 


835/^ 


27 


813/^2 


16I/16 


33^^ 


72 


2iyz2 


4221.^4 


84*1/64 


28 


845/64 


1713/32 


3413/16 


73 


2ll%2 


425 %4 


8521/2 


29 


9/64 


l81/^2 


36/16 


74 


2l21y^2 


432/64 


8621/2 


30 


9^6 


1841/64 


371/64 


75 


2X5 %4 


4353/4 


8721/2 


31 


9% 


191^^4 


3831/64 


76 


225,^2 


442/64 


8821/32 


32 


95 %4 


192^2 


391/6 


77 


22I/32 


4453/4 


894/64 


33 


io7;^2 


202%4 


405/64 


78 


2221/^2 


45/1 6 


9054 


34 


I0l%2 


2I%4 


423/^2 


79 


2257/64 


455/64 


9ii%2 


35 


105^4 


2l21/^2 


43i%4 


80 


239/64 


469/2 


92?l6 


36 


JlM 


22l.i 


44/2 


81 


233/8 


463/ 


933^4 


37 


iimi 


222 %2 


451/6 


82 


2339/4 


4715/64 


94i%2 


38 


Il2 3/^2 


23/6 


465.^ 


83 


2355/64 


4745/4 


9513/^2 


39 


12^4 


24H2 


48/16 


84 


243/32 


481/64 


9623/4 


40 


I2M6 


245/i 


49H 


85 


2421/4 


4841/4 


97?^2 


41 


123 9/64 


25%2 


50^6 


86 


2435/4 


493/32 


9813/4 


42 


122 %2 


255/64 


513 9/64 


87 


2425/2 


49?i6 


99% . 


43 


133/6 


2625/64 


522 5/fe 


88 


25 


50/64 


IOO%2 


44 


1331/^4 


2631/^2 


531 /l 6 


89 


251 5/4 


501/32 


I0015/6 


45 


1325/^2 


273^^4 


55^/^4 


90 


2529/64 


502 %2 


1015^4 



Chords 



89 




Fig. 35. 



To Find the Length of a Chord which will Divide the Circumference of 
a Circle into N Equal Parts Multiply S by the Diameter 



N 


5 


N 


5 


N 


5 


N 


5 


I 




26 


. 12054 


51 


.061560 


76 


041325 


2 




27 


.11609 


52 


.060379 


77 


040788 


3 


'! 86603" 


28 


.11197 


53 


.059240 


78 


040267 


4 


.70711 


29 


. 10812 


54 


.058145 


79 


039757 


5 


.58779 


30 


.10453 


55 


.057090 


80 


039260 


6 


.50000 


31 


.10117 


56 


.056071 


81 


038775 


7 


.43388 


32 


.098018 


57 


.055089 


82 


038303 


8 


.38268 


33 


.095056 


58 


.054139 


83 


037841 


9 


.34202 


34 


.092269 


59 


.053222 


84 


037391 


10 


.30902 


35 


.089640 


60 


.052336 


85 


036953 


II 


.28173 


36 


.087156 


61 


.051478 


86 


036522 


12 


.25882 


37 


.084804 


62 


.050649 


87 


036103 


13 


.23932 


38 


.082580 


63 


.049845 


88 


035692 


14 


.22252 


39 


.080466 


64 


.049068 


89 


035291 


IS 


.20791 


40 


.078460 


65 


.048312 


90 


034899 


16 


.19509 


41 


.076549 


66 


.047582 


91 


034516 


17 


.18375 


42 


.074731 


67 


.046872 


92 


034141 


18 


.17365 . 


43 


.072995 


68 


.046184 


93 


033774 


19 


.16460 


44 


.071339 


69 


.045515 


94 


033415 


20 


.15643 


45 


.069756 


70 


.044865 


95 


033064 • 


21 


.14904 


46 


.06S243 


71 


.044232 


96 


032719 


22 


.14232 


47 


.066793 


72 


.043619 


97 


032381 


23 


.13617 


48 


.065401 


73 


.043022 


98 


032051 


24 


.13053 


49 


.064073 


74 


.042441 


99 


031728 


25 


.12533 


50 


.062791 


75 


.041875 


100 


031411 



90 



Mathematical Tables 



Lengths of Chords for Spacing Circle whose Diameter is i 

For circles of other diameters multiply length given in table by diameter of circle. 



No. of 


Length of 


No. of 


Length of 


No. of 


Length of 


No. of 


Length of 


spaces 


chord 


spaces 


chord 


spaces 


chord 


spaces 


chord 






26 


.1205 


51 


.0616 


76 


.0413 
.0408 
.0403 






27 


.1161 


52 


.0604 


77 


3 


"'■.8660" 


28 


.1120 


53 


.0592 


78 


4 


.7071 


29 


.1081 


54 


.0581 


79 


.0398 


s 


.5878 


30 


.1045 


55 


.0571 


80 


.0393 


6 


.5000 


31 


.1012 


56 


.0561 


81 


.0388 


7 


.4339 


32 


.0980 


57 


.0551 


82 


.0383 


8 


.3827 


33 


.0951 


58 


.0541 


83 


.0378 


9 


.3420 


34 


.0923 


59 


.0532 


84 


.0374 


lo 


.3090 


35 


.0896 


60 


.0523 


85 


.0370 


II 


.2817 


36 


.0872 


61 


.0515 


86 


.0365 


12 


.2588 


37 


.0848 


62 


.0507 


87 


.0361 


13 


.2393 


38 


.0826 


63 


.0499 


88 


.0357 


14 


.2225 


39 


.0805 


64 


.0491 


89 


.0353 


15 


.2079 


40 


.0785 


65 


.0483 


90 


.0349 


i6 


.1951 


41 


.0765 


66 


.0476 


91 


.0345 


17 


.1838 


42 


.0747 


67 


.0469 


92 


.0341 


I8 


.1736 


43 


•0730 


68 


.0462 


93 


.0338 


19 


.1646 


44 


.0713 


69 


.0455 


94 


.0334 


20 


.1564 


45 


.0698 


70 


.0449 


95 


.0331 


21 


.1490 


46 


.0682 


71 


.0442 


96 


.0327 


22 


.1423 


47 


.0668 


72 


.0436 


97 


.0324 


23 


.1362 


48 


.0654 


73 


.0430 


98 


.0321 


24 


.1305 


49 


.0641 


74 


.0424 


99 


.0317 


25 


.1253 


50 


.0628 


75 


.0419 


TOO 


.0314 



Computed by W. I. Mann, Pittsburg, Pa. 
Supplement to Machinery, February, 1903. 



Board Measure 



91 



Board Measure 











Length 


in feet 






Size 


12 


14 


16 


18 


20 


22 


24 


26 




Square feet 


IX 8 


8 


9\i 


I02/^ 


12 


n\i 


142/^ 


16 


17% 


IX 10 


10 


11% 


132/^ 


15 


16% 


18% 


20 


21% 


1X12 


12 


14 


16 


18 


20 


22 


24 


26 


1X14 


14 


16I/6 


182/3 


21 


233'^ 


252/^ 


28 


30% 


IX16 


16 


I82/^ 


21H 


24 


262/^ 


29/3 


32 


34% 


2X 3 


6 


7 


8 


9 


10 


II 


12 


13 


2X 4 


8 


m 


1024 


12 


I3H 


142% 


16 


17% 


2X 6 


12 


14 


16 


18 


20 


22 


24 


26 


2X 8 


16 


18% 


21/3 


24 


262/^ 


29% 


32 


34% 


2X10 


20 


231/^ 


26% 


30 


33H 


3624 


40 


43% 


2X12 


24 


28 


32 


36 


40 


44 


-48 


52 


2X14 


28 


322/^ 


37^ 


42 


4624 


51% 


56 


60% 


2X16 


32 


375^ 


42% 


48 


53H 


582% 


64 


69% 


3X 4 


12 


14 


16 


18 


20 


22 


24 


26 


3X 6 


18 


21 


24 


27 


30 


33 


36 


39 


3X 8 


24 


28 


32 


36 


40 


44 


48 


52 


3X10 


30 


35. 


40 


45 


50 


55 


60 


65 


3X12 


36 


42 


48 


54 


60 


66 


72 


78 


3X14 


42 


49 


S6 


63 


70 


77 


84 


91 


3X16 


48 


56 


64 


72 


80 


88 


96 


104 


4X 4 


16 


I82/^ 


2m 


24 


26% 


29% 


32 


34% 


4X 6 


24 


28 


32 


2,^ 


40 


44 


48 


52 


4X 8 


32 


37H 


42% 


48 


53H 


58% 


64 


69% 


4X10 


40 


46% 


53H 


60 


66% 


73% 


80 


86% 


4X12 


48 


56 


64 


72 


80 


88 


96 


104 


4X14 


56 


65!/^ 


742/3 


84 


93% 


I022/^ 


112 


121% 


4X16 


64 


742/3 


8sH 


96 


106% 


117% 


128 


138% 


6X 6 


36 


42 


48 


54 


60 


66 


72 


78 


6X 8 


48 


56 


64 


72 


80 


88 


96 


104 


6X10 


60 


70 


80 


90 


100 


no 


120 


130 


6X12 


72 


84 


96 


108 


120 


132 


144 


156 


6X14 


84 


98 


112 


126 


140 


154 


168 


182 


6X16 


96 


112 


128 


144 


160 


176 


192 


208 


8X 8 


64 


74% 


851/3 


96 


10624 


117% 


128 


138% 


8X10 


80 


93H 


106% 


120 


133% 


1462% 


160 


173% 


8X12 


96 


112 


128 


144 


160 


176 


192 


208 


8X14 


■112 


I302/^ 


149^/^ 


168 


1862/3 


205% 


224 


242% 


8X16 


128 


I49V^ 


I702/^ 


192 


213% 


234% 


256 


277% 


loXio 


100 


116% 


133^/^ 


150 


1662/3 


183% 


200 


216% 


10X12 


120 


140 


160 


.180 


200 


220 


240 


260 


10X14 


140 


163H 


1862/^ 


210 


233% 


256% 


280 


303% 


10X16 


160 


1862/^ 


213H 


240 


2662/3 


293% 


320 


346% 


12X12 


144 


168 


192 


216 


240 


264 


288 


312 


12X14 


168 


196 


224 


252 


280 


308 


336 


364 


12X16 


192 


224 


256 


288 


320 


352 


384 


416 


14X14 


196 


22m 


2(>m 


294 


326% 


359% 


392 


424% 


14X16 


224 


261H 


2982/i 


336 


373/3 


4io2/^ 


448 


485% 


16x16 


256 


2982/3 


341H 


384 


4262/^ 


469% 


512 


554% 



92 



Mathematical Tables 
Board Measure — {Continued) 





Length in feet 


Size 


28 


30 


32 


34 


36 


38 


40 




Square feet 


IX 8 


i8H 


20 


21 1/^ 


22% 


24 


2534 


26% 


IXIO 


23H 


25 


262/^ 


28H 


30 


312/6 


33H 


IXI2 


28 


30 ■ 


32 


34 


36 


38 


40 


1X14 


322/^ 


35 


37H 


39% 


42 


44I/6 


46% 


1X16 


37H 


40 


42^^ 


45H 


48 


502/6 


53H 


2X 3 


14 


15 


16 


17 


18 


19 


20 


2X 4 


I82/^ 


20 


2ll/i 


222/^ 


24 


25H 


26% 


2X 6 


28 


30 


32 


34 


36 


38 


40 


2X 8 


37^/^ 


40 


422/3 


45H 


48 


502/6 


53% 


2X10 


462/^ 


50 


53H 


56% 


60 


63H 


66% 


2X12 


56 


60 


64 


68 


72 


76 


80 


2X14 


65H 


70 


722/3 


7954 


84 


882/6 


93% 


2X16 


74^i 


80 


85H 


90% 


96 


loii^ 


106% 


3X 4 


28 


30 


32 


34 


36 


38 


40 


3X 6 


42 


45 


48 


51 


54 


57 


60 


3X 8 


56 


60 


64 


68 


72 


76 


80 


3X10 


70 


75 


80 


85 


90 


95 


100 


3X12 


84 


90 


96 


102 


108 


114 


120 


3X14 


98 


los 


112 


119 


126 


133 


140 


3X16 


112 


120 


128 


136 


144 


152 


160 


4X 4 


37H 


40 


42^ 


45H 


48 


50% 


53% 


4X 6 


56 


60 


64 


68 


72 


76 


80 


4X 8 


74^/3 


80 


85!/^ 


9o2/i 


96 


loiH 


106% 


4X10 


93H 


100 


I062/^ 


113H 


120 


126% 


133% 


4X12 


112 


120 


128 


136 


144 


152 


160 


4X14 


130^^ 


140 


ugH 


1582/^ 


168 


177)4 


186% 


4X16 


149H 


160 


\io% 


i8ii/^ 


192 


202% 


213% 


6X 6 


84 


90 


96 


102 


108 


114 


120 


6x 8 


112 


120 


128 


136 


144 


152 


160 


6x10 


140 


150 


160 


170 


180 


190 


200 


6X12 


168 


180 


192 


204 


216 


228 


240 


6x14 


196 


210 


224 


238 


252 


266 


280 


6X16 


224 


240 


256 


272 


288 


304 


320 


8X 8 


U9H 


160 


170^^ 


i8ii.^ 


192 


202% 


213% 


8X10 


1862/^ 


200 


213H 


226% 


240 


253H 


266% 


8X12 


224 


240 


256 


272 


288 


304 


320 


8X14 


261 1/^ 


280 


29824 


317^/^ 


336 


354% 


373% 


8X16 


298^^ 


320 


341I4 


3622/ 


384 


405H 


426% 


loXio 


2335'^ 


250 


266^^ 


283H 


300 


316% 


333% 


10X12 


280 


300 


320 


340 


360 


380 


400 


10X14 


3262/i 


350 


373H 


3962/6 


410 


443H 


466% 


10X16 


373H 


400 


4262yi 


453H 


480 


So6% 


533% 


12x12 


336 


360 


384 


408 


432 


456 


480 


12X14 


392 


420 


448 


476 


504 


532 


560 


12X16 


448 


480 


512 


544 


576 


608 


640 


14X14 


457!/^ 


490 


5222/^ 


S55I/6 


588 


620% 


6S3% 


14X16 


522^/^ 


560 


597H 


634% 


672 


709H 


746% 


16X16 


597I4 


640 


682H 


725H 


768 


810% 


853% 



Note. — By simply multiplying or dividing the above amounts, the number of 
feet contained in other dimensions can be obtained. 



Surface and Volumes of Spheres 93 

Weight of Lumber per iooo Feet Board Measure 



Character of lumber 


Dry 


Partly 
seasoned 


Green • 


Pine and. hemlock 


Pounds 
2500 
3000 
4000 
3SOO 


Pounds 
2750 
4000 
5000 
4CXX) 


Pounds 
3000 


Norway and. yellow pine 


5000 


Oak and walnut ... 













Surface and Volumes of Spheres 

Spheres. (Original.) Trautwine. 
Some errors of i in the last figure only. 



Diam. 


Surface 


Solidity 


Diam. 


Surface 


Solidity 


Diam. 


Surface 


Solidity 


K4 


.0C077 




13/^2 


3.7583 


.68511 


2%2 


15.466 


5.7190 


H2 


.00307 


.00002 


% 


3.9761 


.74551 


M 


15.904 


5. 9641 


%4 


.00690 


.00005 


5/2 


4.2000 


.80939 


%2 


16.349 


6.2161 


Me 


.01227 


.00013 


Me 


4.4301 


.87681 


Me 


16.800 


6. 4751 


3.^2 


.02761 


.00043 


%2 


4.6664 


.94786 


1H2 


17.258 


6.7412 


H 


.04909 


.00102 


M 


4.9088 


1.0227 


% 


17.721 


7.0144 


5i2 


.07670 


.00200 


%2 


5.1573 


I . 1013 


13/^2 


18.190 


7.2949 


3/16 


.11045 


.00345 


Me 


5.4119 


I. 1839 


Me 


18.666 


7.5829 


%2 


. 1S033 


.00548 


1/32 


5.6728 


1.2704 


15/32 


19.147 


7.8783 


}i 


.19635 


.00818 


3/i 


5. 9396 


1.3611 


1/^ 


19.635 


8.1813 


%2 


.24851 


.01165 


13/^2 


6.2126 


I. 4561 


li^2 


20.129 


8.4919 


Me 


.30680 


.01598 


Me 


6.4919 


1-5553 


9/16 


20 . 629 


8.8103 


1H2 


.37123 


.02127 


15^2 


6.7771 


1.6590 


19/^2 


21.135 


9.1366 


H 


.44179 


.02761 


¥2 


7.0686 


I. 7671 


% 


21.648 


9.4708 


m2 


51848 


.03511 


1%2 


7.3663 


1.8799 


2H2 


22.166 


9.8131 


Ma 


.60132 


.04385 


9/6 


7.6699 


1.9974 


iMe 


22.691 


10.164 


15^2 


.69028 


.05393 


19/32 


7.9798 


2.1196 


23/2 


23 . 222 


10.522 


Yi 


.78540 


.06545 


% 


8.2957 


2.2468 


% 


23.758 


10.889 


^%2 


88664 


.07850 


21/2 


8.6180 


2.3789 


25/2 


24.302 


11.265 


9/16 


.99403 


.09319 


iMe 


8.9461 


2.5161 


IMe 


24.850 


11.649 


1%2 


1 . 1075 


. 10960 


23^^2 


9.2805 


2.6586 


2%2 


25.405 


12.041 


^A 


I . 2272 


.12783 


3/ 


9.6211 


2.8062 


% 


25.967 


12.443 


21/^2 


1.3530 


. 14798 


2^2 


9.9678 


2.9592 


2 9/2 


26.535 


12.853 


iMe 


1.4849 


.17014 


iMe 


10.321 


3.1177 


IMe 


27.109 


13.272 


2 3/^2 


I . 6230 


.19442 


^^2 


10.680 


3.2818 


31/2 


27.688 


13.700 


% 


I. 7671 


. 22089 


% 


11.044 


3.4514 


3 


28.274 


14.137 


25/^2 


I. 9175 


.24967 


2 9/32 


II. 416 


3.6270 


Me 


29.465 


15.039 


13/16 


2.0739 


.28084 


1M6 


11.793 


3.8083 


H 


30.680 


15.979 


^%2 


2.236s 


.31451 


31/32 


12.177 


3.9956 


Me 


31.919 


16.957 


% 


2.4053 


.35077 


2 


12.566 


4.1888 


M 


33.183 


17.974 


^%2 


2.5802 


.38971 


H2 


12.962 


4.3882 


Me 


34.472 


19.031 


15/6 


2.7611 


.43143 


Me 


13.364 


4.5939 


3/8 


35.784 


20.129 


3^2 


2.9483 


.47603 


3/^2 


13.772 


4.8060 


Me 


37.122 


21.268 


I 


3.1416 


.52360 


H 


14.186 


5.0243 


1/ 


38.484 


22.449 


H2 


3.3410 


.57424 


^2 


14.607 


5.2493 


9/6 


39.872 


23.674 


He 


3.5466 


.62804 


Me 


15.033 


5. 4809 


5/ 


41.283 


24.942 



94 



Mathematical Tables 

Spheres — {Continued) 



Diam. 


Surface 


Solidity 


Diam. 


Surface 


Solidity 
■268.08 


Diam. 


Surface 


Solidity 


31 He 


42.719 


26.254 


8 


201.06 


14^/^ 


671.9s 


1637.9 


% 


44.179 


27.611 


H 


207.39 


280.85 


3/ 


683.49 


1680.3 


1^6 


45.664 


29.016 


H 


213.82 


294.01 


^i 


695.13 


■ 1723.3 


^i 


47.173 


30.466 


% 


220.36 


307.58 


15 


706.85 


1767.2 


15/16 


48.708 


31.96s 


1/2 


226.98 


321.56 


i/i 


718.69 


1811.7 


4 


50.265 


33.510 


% 


233.71 


335.9s 


1/4 


730.63 


1857.0 


Me 


51.848 


35.106 


3/4 


240.53 


350.77 


3/i 


742.65 


1903.0 


5^ 


53.456 


36.751 


'A 


247.45 


366.02 


H2 


754.77 


1949.8 


3/16 


55.089 


38.448 


9 


254.47 


381.70 


5/i 


767.00 


1997.4 


i/i 


56.745 


40.195 


^ 


261.59 


397.83 


3/ 


779-32 


2045.7 


Me 


58.427 


41.994- 


H 


268.81 


414.41 


Ji 


791.73 


2094.8 


?i 


60.133 


43.847 


% 


276.12 


431.44 


16 


804.25 


2144.7 


7/16 


61.863 


45 . 752 


H 


283.53 


448.92 


\i 


816.85 


2195. 3 


1/^ 


63.617 


47.713 


5/i 


291.04 


466.87 


H 


829.57 


2246.8 


9/16 


65.397 


49.729 


3/ 


298.65 


485.31 


% 


842.40 


2299.1 


54 


67.201 


51.801 


% 


306.36 


504.21 


^'i 


855.29 


2352.1 


11/6 


69.030 


53.929 


10 


314.16 


523.60 


% 


868.31 


2406.0 


M 


70.883 


56.116 


% 


322.06 


543.48 


% 


881.42 


2460.6 


13/6 


72.759 


58.359 


H 


330.06 


S63.86 


'A 


894.63 


2516. I 


Ji 


74.663 


60.663 


3/i 


338.16 


S84.74 


17 


907.93 


2572.4 


15/6 


76.589 


63.026 


H 


346.36 


606.13 


i/i 


921.33 


2629.6 


5 


78.540 


65.450 


5/i 


354.66 


628.04 


H 


934.83 


2687.6 


He 


80.516 


67.935 


3/ 


363.05 


650.46 


% 


948.43 


2746.5 


H 


82.516 


70.482 


% 


371.54 


673.42 


Vi 


962.12 


2806.2 


3/16 


84.541 


73.092 


II 


380.13 


696.91 


% 


975-91 


2866.8 


H 


86.591 


75.767 


% 


388.83 


720,95 


% 


989.80 


2928.2 


5/6 


88.664 


78.505 


H 


397.61 


745.51 


'A 


1003.8 


2990. 5 


3.i 


90.763 


81.308 


% 


406.49 


770.64 


18 


1017.9 


3053.6 


7l6 


92.887 


84.178 


1/2 


41S.48 


796.33 


i/i 


1032. I 


3117.7 


H 


95.033 


87.113 


% 


424.56 


822.58 


H 


1046.4 


3182.6 


«/6 


97.205 


90.118 


3/ 


433.73 


849.40 


% 


1060.8 


3248.5 


5/i 


99.401 


93.189 


li 


443.01 


876.79 


H 


1075.2 


3315.3 


iHe 


101.62 


96.331 


12 


452.39 


904.78 


5/i 


1089.8 


3382.9 


% 


103.87 


99.541 


M 


461.87 


933.34 


% 


1104.5 


3451. 5 


13/6 


106.14 


102.82 


Vi 


471.44 


962.52 


% 


1119.3 


3521.0 


% 


108.44 


106.18 


% 


481. II 


992.28 


19 


1134.1 


3591.4 


15/6 


110.75 


109.60 


H2 


490.87 


1022.7 


i/i 


I149.1 


3662.8 


6 


113. 10 


113. 10 


fi 


S00.73 


1053.6 


H 


1164.2 


3735. 


M 


117.87 


120.31 


% 


510.71 


1085.3 


% 


1179.3 


3808.2 


H 


122.72 


127.83 


% 


520.77 


1117.S 


H2 


1194.6 


3882.5 


3/i 


127.68 


135.66 


13 


530.93 


1IS0.3 


A 


1210.0 


3957.6 


1/^ 


132.73 


143.79 


H 


541.19 


1183.8 


% 


1225.4 


4033. 5 


5/^8 


137.89 


152.25 


H 


551.55 


1218.0 


A 


1241.0 


4110.8 


3/4 


143.14 


161.03 


% 


562.00 


1252.7 


20 


1256.7 


4188.8 


j^^ 


148.49 


170.14 


1/2 


572.55 


1288.3 


H 


1272.4 


4267.8 


7 


153.94 


179.59 


% 


583.20 


1324.4 


H 


1288.3 


4347.8 


H 


159.49 


189.39 


% 


593.95 


1361.2 


% 


1304.2 


4428.8 


H 


165.13 


199.53 


% 


604 . 80 


1398.6 


V2 


1320.3 


4510.9 


% 


170.87 


210.03 


14 


615.75 


1436.8 


% 


1336.4 


4593.9 


H 


176.71 


220.89 


% 


626.80 


1475.6 


% 


1352.7 


4677.9 


5/^ 


182.66 


232.13 


H 


637.95 


1515.1 


li 


1369.0 


4763.0 


3/ 


188.69 


243.73 


% 


649.17 


1555-3 


21 


1385. 5 


4849.1 


^i 


194.83 


255.72 


Vi 


660.52 


1596.3 


\i 


1402.0 


4936.2 



Spheres 

Spheres — (Continued) 



95 



Diam. 


Surface 


Solidity 


Diam. 


Surface 


Solidity 


Diam. 


Surface 


Solidity 


2lH 


1418.6 


5,024.3 


21A 


2441. I 


11,341 


345^2 


3739.3 


21,501 


n 


1435.4 


5.113.5 


28 


2463.0 


11.494 


A 


3766.5 


21,736 


H 


1452.2 


5.203.7 


A 


2485.1 


11,649 


% 


3793.7 


21,972 


^A 


1469.2 


5,295.1 


M 


2507.2 


11,805 


A 


3821 . I 


22,210 


% 


1486.2 


5,397.4 


% 


2529.5 


11,962 


35 


3848.5 


22,449 


^ 


1S03.3 


5.480.8 


Vi 


2551. 8 


12,121 


A 


3876.1 


22,691 


22 


1520.5 


5,575.3 


% 


2574.3 


12,281 


H 


3903.7 


22,934 


H 


1537.9 


5,670.8 


% 


2596.7 


12,443 


A 


3931.5 


23,179 


H 


1555.3 


5,767.6 


A 


2619.4 


12,606 


A 


3959.2 


23,425 


% 


1572.8 


5,865.2 


29 


2642 . I 


12,770 


A 


3987.2 


23,674 


H 


1590.4 


5,964.1 


A 


2665.0 


12,936 


% 


4015.2 


23,924 


% 


1608.2 


6,064.1 


}i 


2687.8 


13,103 


A 


4043.3 


24,176 


% 


1626.0 


6,165.2 


34 


2710.9 


13.272 


36 


4071.5 


24,429 


^i 


1643.9 


6,267.3 


A 


2734.0 


13.442 


A 


4099.9 


24,685 


23 


1661.9 


6,370.6 


H 


2757.3 


13.614 


34 


4128.3 


24,942 


H 


1680.0 


6,475.0 


M 


2780.5 


13.787 


A 


4156.9 


25,201 


M 


1698.2 


6,580.6 


A 


2804.0 


13.961 


A 


4185.5 


25,461 


?^ 


1716.5 


6,687.3 


30 


2827.4 


14.137 


A 


4214. I 


25,724 


H 


1735.0 


6,795.2 


A 


2851 . I 


14.315 


% 


4243.0 


25,988 


% 


1753.5 


6,904.2 


A 


2874.8 


14.494 


A 


4271.8 


26,254 


% 


1772. I 


7,014 3 


H 


2898.7 


14.674 


37 


4300.9 


26,522 


% 


1790.8 


7,125.6 


A 


2922.5 


14.856 


A 


4330.0 


26,792 


24 


1809.6 


7,238.2 


% 


2946.6 


15.039 


1/4 


4359.2 


27,063 


?^ 


1828.5 


7,351.9 


% 


2970.6 


15,224 


% 


4388.5 


27,337 


Vi 


1847.5 


7,466.7 


A 


2994.9 


15,411 


A 


4417.9 


27,612 


% 


1866.6 


7,583.0 


31 


3019. I 


15,599 


A 


4447.5 


27,889 


Vi 


1885.8 


7,700.1 


A 


3043.6 


15,788 


% 


4477.1 


28,168; 


H 


1905. I 


7,818.6 


A 


3068.0 


15,979 


A 


4506.8 


28.449 


% 


1924.4 


7,938.3 


y& 


3092.7 


16,172 


38 


4536.5 


28,731 


% 


1943.9 


8,059.2 


Vi 


3117.3 


16,366 


A 


4566.5 


29,016 


25 


1963.5 


8,181.3 


A 


3142. I 


16,561 


H 


4596.4 


29,302 


li 


1983.2 


8,304.7 


% 


3166.9 


16,758 


3/8 


4626.5 


29,590 


H 


2002.9 


8,429.2 


A 


3192.0 


16,957 


A 


4656.7 


29,880 


% 


2022 . 9 


8,554.9 


32 


3217.0 


17.157 


5/8 


4686.9 


30,173 


^ 


2042.8 


8,682.0 


A 


3242.2 


17.359 


3/4 


4717.3 


30,466 


5,^ 


2062 . 9 


8.810.3 


Vi 


3267.4 


17.563 


A 


4747.9 


30,762 


^4 


2083.0 


8,939.9 


% 


3292.9 


17.768 


39 


4778.4 


31,059 


?^ 


2103.4 


9,070.6 


Vi 


3318.3 


17.974 


A 


4809.0 


31,359 


26 


2123.7 


9,202.8 


A 


3343.9 


18,182 


H 


4839.9 


31,661 


\i 


2144.2 


9,336.2 


% 


3369.6 


18,392 


A 


4870.8 


31,964 


H 


2164.7 


9.470.8 


A 


3395.4 


18,604 


A 


4901.7 


32,270 


?i 


2185.5 


9,606.7 


33 


3421.2 


18,817 


A 


4932.7 


32,577 


1/^ 


2206.2 


9,744.0 


A 


3447.3 


19.032 


% 


4964.0 


32,886 


5/i 


2227.1 


9,882.5 


A 


3473.3 


19,248 


% 


4995.3 


33,197 


% 


2248.0 


10,022 


A 


3499.5 


19.466 


40 


5026.5 


33,510 


''A 


2269.1 


10,164 


A 


3525.7 


19,685 


A 


5058.1 


33,826 


27 


2290.2 


10,306 


A 


3552.1 


19.907 


Yi 


5089.6 


34.143 


H 


2311.5 


10,450 


% 


3578.5 


20,129 


A 


5121.3 


34.462 


H 


2332.8 


10,595 


A 


3605.1 


20,354 


A 


5153. I 


34.783 


% 


2354.3 


10,741 


34 


3631.7 


20,580 


A 


5184.9 


35.106 


H 


2375.8 


10,889 


A 


36S8.5 


20,808 


A 


5216.9 


35.431 


5^ 


2397.5 


11,038 


Vi 


3685.3 


21,037 


A 


5248.9 


35,758 


% 


2419.2 


11,189 


A 


3712.3 


21,268 


41 


5281 . I 


36.087 



96 



Mathematical Tables 
Spheres — {Continued) 



Diam. 


Surface 


Solidity 


Diam 


Surface 


Solidity. 


Diam. 


Surface 


Solidity 


41^ 


S313.3 


36.418 


47% 


7163. I 


57,006 


5A% 


9,288.5 


84.177 


% 


5345.6 


36,751 


% 


7200.7 


57,455 


i/i 


9,331.2 


84,760 


% 


5378.1 


37,086 


48 


7238.3 


57,906 


H 


9,374.1 


85,344 


^ 


5410.7 


37.423 


H 


7276.0 


58,360 


% 


9,417.2 


85.931 


% 


5443.3 


37.763 


Vi 


7313.9 


58.815 


A 


9,460.2 


86,521 


% 


5476.0 


38,104 


% 


7351.9 


59,274 


55 


9.503.2 


87.114 


% 


5508.9 


38,448 


V2 


7389.9 


59.734 


H 


9.546.5 


87.709 


42 


5541.9 


38,792 


% 


7428.0 


60,197 


H 


9,590.0 


88,307 


% 


5574.9 


39.140 


H 


7466.3 


60,663 


H 


9.633.3 


88.908 


H 


5608.0 


39,490 


% 


7504.5 


61,131 


Yi 


9.676.8 


89.511 


H 


5641.3 


39.841 . 


49 


7543.1 


61,601 


n 


9.720.6 


90.117 


Vi 


5674.5 


40,194 


H 


7581.6 


62,074 


% 


9,764.4 


90,726 


% 


5708.0 


40.551 


H 


7620.1 


62,549 


A 


9,808.1 


91,338 


% 


5741.5 


40,908 


H 


7658.9 


63,026 


56 


9,852.0 


91,953 


'A 


5775.2 


41,268 


H 


7697.7 


63,506 


H 


■9.896.0 


92.570 


43 


5808.8 


41,630 


% 


7736.7 


63,989 


M 


9,940.2 


93,190 


i/i 


5842.7 


41,994 


% 


7775 • 7 


64.474 


% 


9.984.4 


93.812 


H 


5876. 5 


42,360 


li 


7814.8 


64,961 


¥2 


10,029 


94.438 


% 


5910.7 


42,729 


50 


7854.0 


65,450 


% 


10,073 


95,066 


Vi 


5944.7 


43,099 


H 


7893.3 


65,941 


% 


10.118 


95,697 


H 


5978.9 


43,472 


Vi 


7932.8 


66,436 


■A 


10,163 


96.330 


H 


6013.2 


43,846 


3/8 


7972.2 


66,934 


SI 


10,207 


96,967 


li 


6047.7 


44.224 


V2 


8011.8 


67.433 


H 


10,252 


97,606 


44 


6082.1 


44,602 


^A 


8051 . 6 


67,935 


H 


10,297 


98,248 


H 


6116.8 


44,984 


% 


8091.4 


68,439 


% 


10,342 


98.893 


'A 


6151.5 


45,367 


A 


8131.3 


68,946 


V2 


10.387 


99,541 


H 


6186.3 


45.753 


51 


8171.2 


69.456 


% 


10,432 


100,191 


H 


6221 . 2 


46.141 


% 


8211.4 


69,967 


% 


10.478 


100,84s 


% 


6256.1 


46,530 


M 


8251 . 6 


70,482 


7/8 


10.523 


101,501 


% 


6291 . 2 


46,922 


^/i 


8292.0 


70,999 


58 


10,568 


102,161 


% 


6326.5 


47,317 


Vi 


8332.3 


71,519 


H 


10,614 


102,823 


45 


6361.7 


47.713 


5/8 


8372.8 


72,040 


H 


10,660 


103,488 


% 


6397.2 


48,112 


% 


8413.4 


72,56s 


% 


10,706 


104,155 


H 


6432.7 


48,513 


% 


8454.1 


73,092 


/2 


10,751 


104,826 


% 


6468.3 


48,916 


52 


8494.8 


73,622 


% 


10,798 


105.499 


H 


6503.9 


49.321 


Vs 


8535.8 


74,154 


% 


10,844 


106,17s 


54 


6539.7 


49.729 


H 


8576.8 


74.689 


% 


10,890 


106.854 


H 


6575.5 


50,139 


y& 


8617.8 


75.226 


59 


10,936 


107,536 


% 


6611.6 


50,551 


K2 


8658.9 


75,767 


i/i 


10,983 


108,221 


46 


6647.6 


50,965 


5/8 


8700.4 


76,309 


H 


11,029 


108,909 


H 


6683.7 


51,382 


% 


8741.7 


76.854 


% 


11,076 


109,600 


H 


6720.0 


51,801 


% 


8783.2 


77,401 


V2 


11,122 


110,294 


% 


6756.5 


52,222 


53 


8824.8 


77,952 


54 


11,169 


110,990 


Vi 


6792.9 


52,645 


Ks 


8866.4 


78,505 


% 


11,216 


111,690 


H 


6829.5 


53,071 


Vi 


8908.2 


79,060 


A 


11,263 


112,392 


% 


6866.1 


53,499 


% 


8950.1 


79,617 


60 


11,310 


113,098 


% 


6902.9 


53,929 


Vi 


8992.0 


80,178 


/8 


11.357 


113.806 


47 


6939 -9 


54.362 


% 


9034.1 


80,741 


/4 


11,404 


114,518 


% 


6976.8 


54,797 


% 


9076.4 


81,308 


34 


11.452 


115,232 


H 


7013.9 


55,234 


% 


9118.5 


81,876 


/2 


11,499 


115,949 


H 


7050.9 


55,674 


54 


9160.8 


82,448 


% 


11.547 


116,669 


H 


7088.3 


56,115 


i/i 


9203.3 


83,021 


M 


11,595 


117.392 


^ 


7125.6 


56.559 


Yi 


9246.0 


83,598 


^i 


11,642 


118,118 



Spheres 
Spheres — (Continued) 



97 



Diam. 


Surface 


Solidity 


Diam. 


Surface 


Solidity 


Diam. 


Surface 


Solidity 


6i 


11,690 


118,847 


67^^ 


14,367 


161,927 


74H 


17,320 


214.333 


H 


11,738 


"9,579 


M 


14.420 


162,827 


% 


17,379 


215,417 


H 


11,786 


120,315 


% 


14,474 


163.731 


Vi 


17,437 


216,505 


H 


11,834 


121,053 


68 


14,527 


164.637 


% 


17,496 


217,597 


H 


11,882 


121,794 


H 


14,580 


165,547 


% 


17,554 


218,693 


H 


11,931 


122,538 


H 


14,634 


166,460 


% 


17,613 


219,792 


Yi 


11,980 


123,286 


H 


. 14,688 


167,376 


75 


17,672 


220,894 


% 


12,028 


124,036 


H 


14,741 


168,295 


\i 


17.731 


222,001 


62 


12,076 


124,789 


5/i 


14,795 


169,218 


M 


17,790 


223.111 


i/i 


12,126 


125,545 


H 


14,849 


170,145 


% 


17,849 


224,224 


H 


12,174 


126,305 


% 


14,903 


171,074 


H 


17.908 


225,341 


H 


12,223 


127,067 


69 


14,957 


172,007 


^A 


17,968 


226,463 


\i 


12,272 


127,832 


H 


15,012 


172,944 


% 


18,027 


227,588 


% 


12,322 


128,601 


H 


15.066 


173,883 


'A 


18,087 


228,716 


% 


12,371 


129,373 


H 


15,120 


174,828 


76 


18,146 


229,848 


% 


12,420 


130,147 


H 


15,175 


175,774 


\^ 


18,206 


230,984 


63 


12,469 


130,925 


■H 


15,230 


176,723 


M 


18,266 


232,124 


i/i 


12,519 


131,706 


H 


15,284 


177,677 


H 


18,326 


233.267 


M 


12,568 


132,490 


n 


15,339 


178,635 


H 


18,386 


234,414 


% 


12,618 


133,277 


70 


15,394 


179.595 


H 


18,446 


235.566 


H 


12,668 


134,067 


Vs 


15,449 


180,559 


H 


18,506 


236,719 


H 


12,718 


134,860 


H 


15,504 


181,525 


Vs 


18,566 


237,879 


% 


12,768 


135,657 


H 


15,560 


182,497 


77 


18,626 


239,041 


% 


12,818 


136,456 


V2 


15,615 


183,471 


Vs 


18,687 


240,206 . 


64 


12,868 


137,250 


5/8 


15,670 


184,449 


\i 


18,748 


241.376 


H 


12,918 


138,065 


% 


15,726 


185,430 


H 


18,809 


242.551 


H 


12,969 


138,874 


Vs 


15,782 


186,414 


H 


18,869 


243,728 


3/i 


13,019 


139,686 


71 


15,837 


187,402 


5/8 


18,930 


244,908 


V^ 


13,070 


140,501 


H 


15,893 


188,394 


M 


18,992 


246,093 


H 


13,121 


141,320 


H 


15,949 


189,389 


% 


19.053 


247,283 


% 


13,172 


142,142 


H 


16,005 


190,387 


78 


19,114 


248,47s 


H 


13,222 


142,966 


3/2 


16,061 


191,389 


Vs 


19-175 


249.672 


6s 


13,273 


143,794 


^yi 


16,117 


192,395 


Vi 


19,237 


250,873 


H 


13,324 


144,625 


M 


16,174 


193,404 


% 


19,298 


252,077 


H 


13,376 


145,460 


% 


16,230 


194,417 


H 


19.360 


253.284 


H 


13,427 


146,297 


72 


16,286 


195,433 


% 


19,422 


254.496 


H 


13,478 


147,138 


H 


16,343 


196,453 


% 


19,483 


255.713 


% 


13,530 


147,982 


H 


16,400 


197,476 


'A 


19,545 


256,932 


% 


13,582 


148,828 


% 


16,456 


198,502 


79 


19,607 


258,15s 


% 


13,633 


149,680 


1/2 


16,513 


199,532 


\^ 


19,669 


259.383 


66 


13,685 


150,533 


5/i 


16,570 


200,566 


M 


19,732 


260,613 


H 


13,737 


151,390 


% 


16,628 


201,604 


% 


19,794 


261,848 


M 


13,789 


152,251 


78 


16,685 


202,645 


Yi 


19,856 


263,088 


% 


13,841 


153,114 


73 


16,742 


203,689 


H 


19-919 


264.330 


H 


13,893 


153,980 


H 


16,799 


204,737 


H 


19,981 


265.577 


5i 


13,946 


154,850 


H 


16,857 


205,789 


li 


20,044 


266,829 


% 


13,998 


155,724 


% 


16,914 


206,844 


80 


20,106 


268,083 


% 


14,050 


156,600 


H 


16,972 


207,903 


A 


20,170 


269.342 


67 


14,103 


157,480 


% 


17,030 


208,966 


H 


20,232 


270,604 


H 


14,156 


158,363 


M 


17,088 


210,032 


H 


20,296 


271,871 


M 


14,208 


159,250 


li 


17,146 


211,102 


H 


20,358 


273,141 . 


% 


14.261 


160,139 


74 


17,204 


212,175 


H 


20,422 


274,416 


H 


14,314 


161,032 


H 


17,262 


213,252 


% 


20,485 


275,694 



98 



Mathematical Tables 
Spheres — {Continued) 



Diam. 


Surface 


Solidity 


Diam. 


Surface 


Solidity 


Diam. 


Surface 


Solidity 


8o7^ 


2o,549 


276,977 


s^% 


23,984 


349,269 


93^/^ 


27,686 


433.160 


81 


20,6l2 


278,263 


H 


24,053 


350,771 


94 


27.759 


434.894 


H 


20,676 


279-553 


% 


24,122 


352,277 


H 


27.833 


436,630 


y. 


20,740 


280,847 


% 


24,191 


353,785 


H 


27.907 


438,373 


% 


20,804 


282,14s 


7/i 


24,260 


355.301 


% 


27,981 


440,118 


H 


20,867 


283.447 


88 


24,328 


356,819 


H 


28,055 


441,871 


H 


20,932 


284,754 


H 


24,398 


358,342 


% 


28,130 


443,62s 


% 


20,996 


286,064 


H 


24,467 


359,869 


% 


28,204 


445,387 


^ 


21,060 


287,378 


H 


24.536 


361,400 


% 


28,278 


447,151 


82 


21,124 


288,696 • 


H 


24.606 


362,935 


95 


28,353' 


448,920 


H 


21,189 


290,019- 


% 


24,676 


364,476 


H 


28,428 


450,69s 


H 


21,253 


291.34s 


% 


24,745 


366,019 


\i 


28,503 


452,475 


H 


21,318 


292,674 


A 


24,815 


367,568 


% 


28,577 


454,259 


H 


21,382 


294,010 


89 


24,885 


369,122 


Vi 


28,652 


456,047 


% 


21,448 


295,347 


}i 


' 24,955 


370,678 


n 


28,727 


457,839 


% 


21,512 


296,691 


H 


25,025 


372,240 


% 


28,802 


459,638 


% 


21,578 


298,036 


9i 


25,095 


373,806 


% 


28,878 


461,439 


83 


21,642 


299,388 


i/i 


25.165 


375,378 


96 


28,953 


463,248 


H 


21,708 


300,743 


H 


25,236 


376,954 


% 


29,028 


465,059 


H 


21,773 


302,100 


% 


25,306 


378,531 


H 


29,104 


466,87s 


. % 


21,839 


303.463 


% 


25,376 


380,11s 


H 


29,180 


468,697 


H 


21,904 


304,831 


90 


25,447 


381,704 


V2 


29,25s 


470,524 


% 


21,970 


306,201 


H 


25,518 


383.297 


n 


29,331 


472,354 


H 


22,036 


307,576 


H 


25,589 


384,894 


% 


29.407 


474,189 


Vs 


22,102 


308,957 


H 


25,660 


386,496 


A 


29,483 


476,029 


84 


22,167 


310,340 


H 


25,730 


388,102 


97 


29,559 


477,874 


H 


22,234 


311,728 


5/i 


25,802 


389,711 


H 


29,636 


479.725 


H 


22,300 


313.118 


H 


25,873 


391,327 


H 


29,712 


481,579 


% 


22,366 


314.514 


li 


25,944 


392,945 


% 


29,788 


483,438 


H 


22,432 


315.915 


91 


26,016 


394,570 


H 


29,865 


485,302 


^A 


22,499 


317.318 


Vs 


26,087 


396,197 


5/i 


29,942 


487,171 


% 


22,565 


318,726 


H 


26,159 


397,831 


% 


30,018 


489,04s 


% 


22,632 


320,140 


H 


26,230 


399.468 


% 


30.09s 


490,924 


8s 


22,698 


321,556 


H 


26,302 


401,109 


98 


30,172 


492,808 


H 


22,765 


322,977 


^A 


26,374 


402,756 


% 


30.249 


494,695 


H 


22,832 


324.402 


% 


26,446 


404,406 


H 


30.326 


496,588 


H 


22,899 


325,831 


A 


26,518 


406,060 


34 


30,404 


498,486 


H 


22,966 


327.264 


92 


26,590 


407,721 


H 


30,481 


500,388 


^A 


23.034 


328,702 


H 


26,663 


409,384 


H 


30,558 


502,296 


H 


23,101 


330,142 


M 


26,735 


4II.OS4 


% 


30,636 


S04.208 


% 


23,168 


331.588 


H 


26,808 


412,726 


78 


30.713 


506,12s 


86 


23.23s 


333.039 


V2 


26,880 


414,405 


99 


30,791 


508,047 


H 


23,303 


334,492 


H 


26,953 


416,086 


A 


30,869 


S09.975 


H 


23.371 


335,951 


% 


27,026 


417,774 


Vi 


30,947 


511,906 


H 


23,439 


337,414 


% 


27.099 


419,464 


% 


31,025 


S13.843 


H 


23.506 


338,882 


93 


27.172 


421,161 


H 


31,103 


SIS. 78s 


H 


23,575 


340,352 


H 


27.245 


422,862 


H 


31,181 


517,730 


H 


23,643 


341.829 


H 


27,318 


424,567 


H 


31.259 


S19.682 


% 


23.711 


343,307 


H 


27,391 


426,277 


% 


31.338 


521,638 


87 


23.779 


344,792 


H 


27,464 


427,991 


100 


31.416 


523.598 


H 


23.847 


346,281 


% 


27,538 


429,710 








H 


23.916 


347,772 


H 


27,612 


431,433 









Capacity of Rectangular Tanks 



99 



Capacity of Rectangular Tanks in U. S. Gallons for 
Each Foot in Depth 



Width of 
tank 



Ft. Ins. 

2 

2 6 
3 

3 6 
4 

4 6 
5 

5 6 
6 



Length of tank 



2 feet 



2 feet, 
6 ins. 



3 feet 



3 feet, 
6 ins. 



52.36 
65.45 
78.54 
91.64 



4 feet 



4 feet, 
6 ins. 



67.32 
84.16 
100.99 
117.82 
134.65 
151.48 



Sfeet 



74.81 
93.51 
112. 21 
130.91 
149.61 
168.31 
187.01 



5 feet, 

6 ins. 



82.29 
102.86 
123.43 
144.00 
164.57 
185.14 
205.71 
226.28 



6 feet 



89.77 
112. 21 
134.65 
157.09 
179.53 
201.97 
224.41 
246.86 
269.30 









Length of tank 






Width of 














tank 
















6 feet, 6 ins. 


7 feet 


7 feet, 6 ins. 


8 feet 


8 feet, 6 ins. 


9 feet 


Ft. Ins. 














2 


97.2s 


104.73 


112. 21 


119.69 


127.17 


134.6s 


2 6 


121.56 


130.91 


140.26 


149.61 


158.96 


168.31 


3 


145.87 


157.09 


168.31 


179-53 


190.75 


202.97 


3 6 


170.18 


183.27 


196.36 


209.45 


222.54 


235.63 


4 


194.49 


209.45 


224.41 


239-37 


254.34 


269.30 


4 6 


218.80 


235.63 


252.47 


269.30 


286.13 


302.96 


5 


243.11 


261.82 


280.52 


299-22 


317.92 


336.62 


5 6 


267.43 


288.00 


308.57 


329-14 


349.71 


370.28 


6 


291.74 


314.18 


336.62 


359 06 


381.50 


403.94 


6 6 


316.05 


340.36 


364.67 


388.98 


413.30 


437.60 


7 




366.54 


392 . 72 


418 91 


455.09 

476 88 


471.27 
S04.93 
538.59 
572.25 
605.92 


7 6 






420 . 78 


448 83 


8 








478 75 


508.67 
540.46 


8 6 










9 























lOO 



Mathematical Tables 



Capacity of Rectangular Tanks in U. S. Gallons for 
Each Foot in Depth — {Continued) 





Length of tank 


Width of 














tank 


9 feet, 




10 feet, 




II feet. 






6 ins. 


10 feet 


6 ins. 


II feet 


6 ins. 


12 feet 


Ft. Ins. 














2 


142.13 


149.61 


157.09 


164-57 


172. OS 


179. S3 


2 6 


177.66 


187.01 


196.36 


205.71 


215.06 


224.41 


3 


213.19 


224.41 


235.68 


246.86 


258.07 


269.03 


3 6 


248.73 


261.82 


274.90 


288.00 


301.09 


314.18 


4 


284.26 


299.22 


314.18 


329-14 


344- 10 


359 -06 


4 6 


319.79 


336.62 


353-45 


370.28 


385.10 


403-94 


5 


355-32 


374.03 


392.72 


411-43 


430.13 


448.83 


5 6 


390. 85 


411.43 


432.00 


452.57 


473-14 


493-71 


6 


426.39 


448.83 


471-27 


493-71 


S16.15 


538.59 


6 6 


461.92 


486.23 


510.54 


534.85 


559.16 


■583.47 


7 


497.45 


523.64 


549.81 


575-99 


602.18 


628.36 


7 6 


523.98 


561.04 


589.08 


617.14 


645.19 


673.24 


8 


568. SI 


598.44 


628.36 


658.28 


688.20 


718.12 


8 6 


604.05 


635.84 


667.63 


699-42 


713-21 


763.00 


9 


639.58 


673.25 


706.90 


740.56 


774-23 


807.89 


9 6 


675.11 


710.65 


746.17 


781.71 


817.24 


852.77 


lO 




748.05 


785.45 


822.86 


860.26 


897.66 


lo 6 






824.73 


864.00 


903-26 


942.56 


II 








905.14 


946 . 27 


987 . 43 


II 6 










989.29 


1032 3 


12 












1077 . 2 















Number of Barrels (31.5 Gallons) in Cisterns and Tanks 

I Bbl. 31.S Gallons 4-2109 Cubic Feet. 





Diameter in feet 


Depth in 


















feet 


5 


6 


7 


8 


9 


10 


II 


12 


I 


4.663 


6.714 


9.139 


11.937 


15.108 


18.652 


22.659 


26.859 


S 


23.3 


36.6 


45. 7 


59.7 


75.5 


93.3 


112. 8 


134.3 


6 


28.0 


40.3 


54.8 


71.6 


90.6 


III. 9 


135.4 


161. 2 


7 


32.6 


47.0 


64.0 


83.6 


105.10 


130.6 


158.0 


188.0 


8 


37.3 


53.7 


73.1 


95.5 


120.9 


149.2 


180.6 


214.9 


9 


42.0 


60.4 


82.3 


107.4 


136.0 


167.9 


203.1 


241.7 


10 


46.6 


67.1 


91.4 


II9-4 


151. 1 


186.5 


225.7 


268.6 


II 


51.3 


73.9 


100.5 


131. 3 


166.3 


205.2 


248.3 


295.4 


12 


56.0 


80.6 


109.7 


143.2 


181. 3 


223.8 


270.8 


322.3 


13 


60.6 


87.3 


118. 8 


152.2 


196.4 


242.5 


293.4 


349.2 


14 


65.3 


94.0 


127.9 


167. 1 


211. s 


261. 1 


316.0 


376.0 


15 


69. Q 


100.7 


137. 1 


179. 1 


226.6 


289.8 


338.5 


402.9 


16 


74.6 


107.4 


146.2 


191. 


241.7 


298.4 


361. 1 


429.7 


17 


79.3 


114. 1 


155.4 


202.9 


256.8 


317. 1 


383.7 


456.6 


18 


83.9 


120.9 


164. 5 


214.9 


271.9 


335.7 


406.2 


483.5 


19 


88.6 


127.6 


173.6 


226.8 


287.1 


354.4 


428.8 


510.3 


20 


93.3 


134.3 


182.8 


238.7 


302.2 


373.0 


451.4 


537.2 



Number of Barrels in Cisterns and Tanks 



lOI 



Number of Barrels (31.5 Gallons) in Cisterns and 
Tanks — {Continued) 











Diameter in feet 








Depth 




















in feet 






















13 


14 


15 


16 


17 


18 


19 


20 


21 


I 


31.522 


36.557 


41.9 


47-7 


53.9 


60.4 


67-3 


74.6 


82.2 


5 


157.6 


182.8 


209.8 


238.7 


269.5 


203.2 


336.7 


373.0 


441.3 


6 


199. 1 


219.3 


251.8 


286.5 


323.4 


362.6 


404.0 


447.6 


493.6 


7 


220.7 


255.9 


293.8 


334.2 


377.3 


423.0 


471.3 


522.2 


575.8 


8 


252 2 


292. 5 


335.7 


382.0 


431-2 


483.4 


538.7 


590.8 


658.0 


9 


283.7 


329.0 


377.7 


429.7 


485.1 


543.9 


606.0 


671.5 


740.3 


10 


315.2 


365.6 


419.7 


477.5 


539.0 


604.3 


673.3 


746.1 


822.5 


II 


346.7 


402.1 


461.6 


525.2 


592.9 


664.7 


740.7 


820.7 


904.8 


12 


378.3 


438.7 


503.6 


573.0 


646.8 


725.2 


808.0 


895.3 


987.0 . 


13 


409.8 


475.2 


545.6 


620.7 


700.7 


785.6 


875.3 


969.9 


1069.3 


14 


441.3 


5II.8 


587.5 


668.5 


754.6 


846.0 


942.6 


1044.5 


II5I.S 


IS 


472.8 


548.4 


629. s 


716.2 


808.5 


906.5 


lOIO.O 


III9.I 


1223.8 


16 


504.4 


584.9 


671.5 


764.0 


862.4 


966.9 


1077.3 


II93.7 


I3I6.0 


17 


535.9 


621.5 


713.4 


811. 7 


916.4 


1027.4 


II44.6 


1268.3 


1398.3 


18 


567.4 


658.0 


755.4 


859.5 


970.3 


1087.8 


I2I2.0 


1342.9 


1480.6 


19 


598.9 


694.6 


797.4 


907.2 


1024.2 


1148.2 


1279-3 


I4I7.5 


1562.8 


20 


630.4 


731. 1 


839-3 


955.0 


1078. I 


1208.6 


1346.6 


1492. I 


1645-1 











Diameter 


nfeet 






Depth in 
















feet 






















22 


23 


24 


25 


26 


27 


28 


29 


30 


I 


90-3 


98.6 


107.4 


116. 6 


126. 1 


136.0 


148.2 


157.9 


167.9 


5 


451 -4 


483.3 


537-2 


582.9 


630.4 


679.8 


731. 1 


784.3 


839.3 


6 


541.6 


592.0 


644.6 


699.4 


756.5 


815.8 


877.4 


941 -I 


1007.2 


7 


631.9 


690.7 


752.0 


816.0 


882.6 


951.8 


1023.6 


1098.0 


1175.0 


8 


722.2 


789.3 


859.5 


932.6 


1008.7 


1087.7 


1169.8 


1254.9 


1342.9 


9 


812.5 


888.0 


966.9 


1049. I 


1134.7 


1223.7 


1316.0 


1411.7 


1510.8 


10 


902.7 


986.7 


1074.3 


1165.7 


1260.8 


1359.7 


1462.2 


1568.6 


1678.6 


II 


993.0 


1085.3 


1181.8 


1282.3 


1386.9 


1495.6 


1608.5 


1725.4 


1846.5 


12 


1083.3 


1184.0 


1289.2 


1398.8 


1513.0 


1631.6 


1764.7 


1882.3 


2014.0 


13 


1173.5 


1282.7 


1396.6 


1515.4 


'1639. 1 


1767.6 


1900.9 


2039.2 


2182.2 


14 


1263.8 


1381.3 


1504.0 


1632.6 


1765.2 


1903.6 


2047.2 


2196.0 


2350.1 


15 


1354. I 


1480.0 


1611.5 


1748.6 


1891.2 


2039.5 


2193-4 


2352.9 


2517.9 


16 


1444.4 


1578.7 


1718.9 


1865. I 


2017.3 


2175.5 


2339.6 


2509.7 


2685.8 


17 


1534.5 


1677.3 


1826.3 


1981.7 


2143.4 


2311.5 


2485.8 


2666.6 


2853-7 


18 


1624.9 


1776.0 


1933.8 


2098.3 


2269.5 


2447.4 


2632.0 


2823.4 


3021.5 


19 


1715.2 


1874.7 


2041 . 2 


2214.8 


2395.6 


2583.4 


2778.3 


2980.3 


3189-4 


20 


180S.5 


1973.3 


2148.6 


2321.4 


2521.7 


2719.4 


2924.5 


3137.2 3357-3 



I02 



Mathematical Tables 



Contents of Cylinders, or Pipes 
Contents for one foot in length, in cubic feet, and in U. S. 
gallons of 231 cubic inches, or 7.4805 gallons to a cubic foot. A cubic 
foot of water weighs about 62H lbs.; and a gallon about 8H lbs. Diams. 
2, 3, or 10 times as great give 4, 9, or 100 times the content. 







For I foot 


in 






For I foot in 






length 








length 




Diam- 
eter in 
decimals 
of a foot 






Diam- 
eter in 
inches 


Diam- 
eter in 
decimals 
of a foot 






Diam- 
eter in 
inches 


Cubic p 
feet. Also \ 


allons 
f 231 


Cubic 
feet. Also 


Gallons 
of 231 






area in 
square -^ 
feet 


ubic 
iches 






area in 

square 

feet 


cubic 
inches 


H 


.0208 


.0003 


.0025 


^ 


.6250 


.3068 


2.29s 


Me 


.0260 


.0005 


.0040 


Vi 


.6458 


.3276 


2.450 


% 


.0313 


.0008 


.0057 


8 


.6667 


.3491 


2.6X1 


Me 


.0365 


.0010 


.0078 


Vi 


.6875 


.3712 


2.777 


\^ 


.0417 


.0014 


0102 


H 


.7083 


.3941 


2.948 


9i6 


.0469 


.0017 


0129 


Vi 


.7292 


.4176 


3.12s 


% 


.0521 


.0021 


0159 • 


9 


.7500 


.4418 


3.30s 


iMe 


.0573 


.0026 


0193 


Vi 


.7708 


.4667 


3.491 


% 


.0625 


.0031 


0230 


H 


.7917 


.4922 


3.682 


m^ 


.0677 


.0036 


0269 


Vi 


.8125 


.5185 


3.879 


li 


.0729 


.0042 


0312 


10 


.8333 


.5454 


4.080 


1^6 


.0781 


.0048 


0359 


Vi 


.8542 


.5730 


4.286 


I 


.0833 


.0055 


0408 


1/2 


.8750 


.6013 


4.498 


M 


.1042 


.0085 


0638 


% 


.8958 


.6303 


4.71S 


H 


.1250 


.0123 


0918 


II 


.9167 


.6600 


4.937 


% 


.1458 


.0167 


1249 


Vi 


■ 9375 


.6903 


5.164 


2 


.1667 


.0218 


1632 


H 


.9583 


.7213 


S.396 


Vi ■ 


.1875 


.0276 


2066 


Vi 


.9792 


.7530 


5.633 


H 


.2083 


.0341 


2550 


12 


I foot 


.7854 


5.87s 


¥i 


.2292 


.0412 


3085 


Vi 


1.042 


.8522 


6. 375 


3 


.2500 


.0491 


3672 


13 


1.083 


.9218 


6.89s 


Vi 


.2708 


.0576 


4309 


\i 


1. 125 


.9940 


7.436 


H 


.2917 


.0668 


4998 


14 


1. 167 


1.069 


7.997 


% 


.3125 


.0767 


5738 


J-i 


1.208 


1. 147 


8.578 


4 


.3333 


.0873 


6528 


15 


1.250 


1.227 


9.180 


H 


.3542 


.0985 


7369 


H 


1.292 


1. 310 


9.801 


Vi 


.3750 


.1104 


8263 


16 


1.333 


1.396 


10.44 


H 


.3958 


.1231 


9206 


1/2 


1.375 


1.485 


II. II 


5 


.4167 


. 1364 I 


020 


17 


1. 417 


1.576 


11.79 


»H 


.4375 


.1503 I 


125 


1/^ 


1-458 


1.670 


12.49 


5^ 


.4583 


. 1650 I 


234 


18 


1.500 


1.767 


13.22 


H 


.4792 


.1803 I 


349 


\^ 


1.542 


1.867 


13.96 


6 


.5000 


.1963 I 


469 


19 


1.583 


1.969 


14.73 


Vi 


.5208 


.2131 I 


594 


M 


1.625 


2.074 


15.51 


\i 


.5417 


.2304 I 


724 


20 


1.667 


2.182 


16.32 


Vi 


.5625 


.2485 I 


859 


H 


1.708 


2.292 


17. IS 


7 


.5833 


.2673 I 


999 


21 


1.750 


2.405 


17.99 


Vi 


.6042 


.2867 2 


145 


M 


1.792 


2. 521 


18.86 



Contents of Cylinders, or Pipes 103 

Contents of Cylinders^ or Pipes — {Continued) 







For I 


foot in 






For I foot in 






length 






length 




Diam- 
eter in 






Diam- 
eter in 




Diam- 






Diam- 






eter in 
inches 


decimals 
of a foot 


Cubic 
feet. Also 


Gallons 
of 231 


eter in 
inches 


decimals 
of a foot 


Cubic 
feet. Also 


Gallons 
of 231 






area m 


cubic 






area in 


cubic 






square 
feet 


inches 






square 
feet 


inches 


22 


1.833 


2.640 


19.75 


35 


2.917 


6.681 


49.98 


M 


1.87s 


2.761 


20.66 


36 


3.000 


7-069 


52.88 


23 


1. 917 


2.88s 


21.58 


37 


3.083 


7.467 


55.86 


^^ 


1.958 


3 012 


22.53 


38 


3.167 


7.876 


58.92 


24 


2.000 


3.142 


23 -SO 


39 


3.250 


8.296 


62.06 


25 


2.083 


3.409 


25.50 


40 


3.333 


8.727 


65.28 


26 


2.1^7 


3.687 


27.58 


41 


3.417 


9.168 


68.58 


27 


2.250 


3.976 


29.74 


42 


3.500 


9.621 


71.97 


28 


2.333 


4.276 


31.99 


43 


3-583 


10.085 


75.44 


29 


2.417 


4.587 


34.31 


44 


3-667 


10. 559 


78.99 


30 


2.500 


4.909 


36.72 


45 


3.750 


II. 04s 


82.62 


31 


2.583 


5.241 


39-21 


46 


3.833 


II. 541 


86.33 


32 


2.667 


5.585 


41.78 


47 


3.917 


12.048 


90.13 


33 


2.750 


5.940 


44-43 


48 


4.000 


12.566 


94.00 


34 


2.833 


6.305 


47-16 













Table 


Continued, but with 


THE DlATVTF.TERS IN FeET 


Diam., 


Cubic 


U.S. 


Diam., 


Cubic 


U.S. 


Diam., 


Cubic 


U.S. 


feet 


feet 


gallons 


feet 


feet 


gallons 


feet 


feet 


gallons 


4 


12.57 


94.0 


8 


50.27 


376.0 


20 


314-2 


2350 


H 


14.19 


106. 1 


H 


56.75 


424.5 


21 


346.4 


2591 


H 


15.90 


119. 


9 


63 .'62 


475-9 


22 


380.1 


2844 


% 


17.72 


132.5 


^A 


70.88 


S30-2 


23 


415-5 


3108 


5 


19.64 


146.9 


10 


78.54 


587-5 


24 


452.4 


3384 


Vi 


21.65 


161. 9 


1/2 


86.59 


647-7 


25 


490.9 


3672 


Vi 


23.76 


177.7 


II 


95.03 


710.9 


26 


530.9 


3971 


H 


25-97 


194.3 


H 


103.90 


777 -o 


27 


572.6 


4283 


6 


28.27 


211. 5 


12 


113. 1 


846.1 


28 


615.8 


4606 


Vi 


30.68 


229.5 


13 


132.7 


992.8 


29 


660.5 


4941 


H 


33-18 


248.2 


14 


153.9 


1152 


30 


706.9 


5288 


H 


35.79 


267.7 


15 


176.7 


1322 


31 


754.8 


5646 


7 


38.49 


287.9 


16 


201. 1 


1S04 


32 


804. » 


6017 


H 


41.28 


308.8 


17 


227.0 


1698 


33 


855.3 


6398 


H 


44.18 


330.5 


18 


254.5 


1904 


34 


907.9 


6792 


H 


47.17 


352.9 


19 


283.5 


2121 


35 


963.1 


7197 



I04 



Mathematical Tables 



Contents of Linings of Wells 

For diameters twice as great as those in the table, for the cubic yards 
of digging, take out those opposite one half of the greater diameter; and 
multiply them by 4. Thus, for the cubic yards in each foot of depth of 
a well 31 feet in diameter, first take out from the table those opposite the 
diameter of 153'^ feet; namely, 6.989. Then 6.989 X 4 = 27.956 cubic 
yards required for the 31 feet diameter. But for the stone lining or 
walling, bricks or plastering, multiply the tabular quantity opposite 
half the greater diameter by 2. Thus, the perches of stone walling for 
each foot of depth of a well of 31 feet diameter will be 2.073 X 2 = 
4.146. If the wall is more or less than one foot thick, within usual 
moderate limits, it will generally be near enough for practice to assume 
that the number of perches, or of bricks, will increase or decrease in the 
same proportion. 

The size of the bricks is taken at 8K X 4 X 2 inches; and to be laid 
dry, or without mortar. In practice an addition of about 5 per cent 
should be made for waste. The brick Hning is supposed to be i brick 
thick, or 8^ ins. 

Caution. — Be careful to observe that the diameters to be used for 
the digging are greater than those for the walling, bricks, or plastering. 





For each foot of depth 




For each foot of depth 




For this 


For these three col- 


For this 


For these three col- 




column 


umns use the diameter 




column ^ 


imns use the diameter 




use the 


in clear of the lining 




use the 


in clear of the lining 


Diam- 


diam- 
eter of 






Diam- 
eter 


diam- 






eter 








eter of 








in 

feet 


the digT 


Stone 
lining 


No. of 




in 
feet 


the dig- j^ 


Jtone 
ning 


No. of 






ging 


I foot 


bricks 


Square 




ging ^ 


foot 


bricks 


Square 






thick. 


- in a 


yards of 
plaster- 






lick. 


• 


yards of 
plaster- 






Perches 


lining 




^ u- P^ 


rches 


lining 




Cubic 


of 25 


I brick 


ing 




Cubic 


3f2S 


I brick 


ing 




yards of 


cubic 


thick 






yards of ^ 


ubic 


thick 






digging 


feet 








digging 


feet 






1 


.0291 


.2513 


57 


.3491 


4 


.4654 


6283 


227 


1.396 


H 


.0455 


.2827 


71 


.4364 


H 


.5254 


6597 


241 


1.484 


\i 


.0654 


.3142 


85 


.5236 


1/2 


.5890 


6912 


255 


1. 571 


H 


.0891 


.3456 


99 


.6109 


H 


:6563 


7226 


269 


1.658 


2 


.1164 


.3770 


114 


.6982 


5 


.7272 


7540 


283 


1-745 


H 


.1473 


.4084 


128 


.7855 


u 


.8018 


7854 


297 


1.833 


H 


.1818 


.4398 


142 


.8727 


1/2 


.8799 


8168 


311 


1.920 


H 


.2200 


.4712 


156 


.9600 


H 


■9617 


8482 


326 


2.007 


3 


.2618 


.5027 


170 


1.047 


6 


1.047 


8796 


340 


2.09s 


H 


• 3073 


.5341 


184 


1. 135 


H 


1. 136 


9111 


354 


2.182 


H 


• 3563 


5655 


198 1.222 


H 


1.229 


9425 


368 


2.269 


H 


.4091 


■5969 


212 1.309 


% 


1.325 


9739 


382 2.356 



A cubic yard = 203 U. S. gallons. 



Contents of Linings of Wells 
Contents or Linings of Wells 



105 





For each foot of depth 




For each foot of depth 




For this 


For these three col- 


For this 


For these three col- 




column 


umns use the diameter 




column 


umns use the diameter 




use the 


in clear of the lining 


Diam- 
eter 


use the 


in clear of the lining 


Diam- 


diam- 
eter of 








diam- 
eter of 






eter 














in 
feet 


the dig- 


Stone 
lining 


No. of 




in 
feet 


the dig- 


Stone 
lining 


. No. of 






ging 


I foot 


bricks 


Square 




ging 


I foot 


bricks 


Square 






thick. 


in a 


yards of 






thick. 


in a 


yards of 












Perches 


lining 


plaster- 






Perches 


lining 


plaster- 




Cubic 


of 25 


I brick 


ing 




Cubic 


of 25 


I brick 


ing 




yards of 


cubic 


thick 






yards of 


cubic 


thick 






digging 


feet 








digging 


feet 






7 


1.42s 


1.005 


396 


2.444 


16H 


7.681 


2.168 


919 


5. 673 


Vi 


1.529 


1.037 


410 


2.531 


1/2 


7.919 


2.199 


933 


5.760 


Vi 


1.636 


1.068 


425 


2.618 


V^ 


8. 161 


2.231 


948 


5.847 


% 


1.747 


1. 100 


439 


2.705 


17 


8.407 


2.262 


962 


5.934 


8 


1.862 


1. 131 


453 


2.793 


H 


8.656 


2.293 


976 


6.022 


K 


1.980 


1. 162 


467 


2.880 


Vi 


8.908 


2.325 


990 


6.109 


H 


2.102 


1. 194 


481 


2.967 


% 


9.165 


2.356 


1004 


6.196 


% 


2.227 


1.225 


495 


3.054 


18 


9.425 


2.388 


1018 


6.283 


9 


2.356 


1.257 


509 


3-142 


M 


9.688 


2.419 


1032 


6.371 


% 


2.489 


1.288 


523 


3.229 


\^ 


9.956 


2.450 


1046 


6.458 


H 


2.625 


1. 319 


538 


3.316 


K 


10.23 


2.482 


1061 


6.545 


% 


2.76s 


1. 351 


552 


3.404 


19 


10.50 


2.513 


I07S 


6.633 


10 


2.909 


1.382 


566 


3.491 


Vi 


10.78 


2.545 


1089 


6.720 


Yi 


3.056 


1. 414 


580 


3.578 


^2 


11.06 


2.576 


1 103 


6.807 


"■A 


3.207 


1.445 


594 


3.665 


% 


11.35 


2.608 


1117 


6.894 


% 


3 362 


1.477 


608 


3.753 


20 


11.64 


2.639 


1131 


6.982 


II 


3.520 


1.508 


622 


3.840 


H 


11.93 


2.670 


1145 


7.069 


Vi ■ 


3.682 


1.539 


637 


3.927 


H 


12.22 


2.702 


1160 


7.156 


1/^ 


3.847 


1. 571 


651 


4.014 


% 


12.52 


2.733 


1174 


-7.243 


¥i 


4.016 


1.602 


665 


4.102 


21 


12.83 


2.765 


1 188 


7.331 


12 


4.189 


1.634 


■679 


4.189 


M 


13.14 


2.796 


1202 


7.418 


• M 


4.36s 


1.665 


693 


4.276 


1/2 


13.45 


2.827 


1216 


7.505 


Vi 


4.545 


1.696 


707 


4.364^ 


% 


13.76 


2.859 


1230 


7.593 


% 


4.729 


1.728 


721 


4.451 


22 


14.08 


2.890 


1244 


7.680 


13 


4.916 


1.759 


736 


4.538 


Yi 


14.40 


2.922 


1259 


7.767 


H 


5. 107 


1. 791 


750 


4.625 


Yi 


14.73 


2.953 


1273 


7.854 


1/^ 


5.301 


1.822 


764 


4.713 


% 


15.06 


2.985 


1287 


7.942 


% 


S-Soo 


1.854 


778 


4.800 


23 


15.39 


3.016 


1301 


8.029 


14 


5.701 


1.885 


792 


4.887 


Yi 


15.72 


3.047 


1315 


8. 116 


\i 


S.907 


1. 916 


806 


4.974 


Yi 


16.06 


3.079 


1329 


8.203 


Y^ 


6. 116 


1.948 


820 


5.062 


% 


16.41 


3. no 


1343 


8.291 


% 


6.329 


1.979 


834 


5.149 


24 


16.76 


3.142 


1357 


8.378 


IS 


6.545 


2. on 


849 


5.236 


H 


17. II 


3.173 


1372 


8.465 


H 


6.765 


2.042 


863 


5.323 


Y. 


17.46 


3.204 


1386 


8.552 


1/^ 


6.989 


2.073 


877 


5. 411 


% 


17.82 


3.236 


1400 


8.640 


% 


7.216 


2.105 


891 


5.498 


25 


18.18 


3.267 


1414 


8.727 


16 


7.447 


2.136 


90s 


5.585 













A cubic yard = 202 U. S. gallons. 



lo6 Mathematical Tables 

If perches are named in a contract, it is necessary, in order to prevent 
fraud, to specify the number of cubic feet contained in the perch; for 
stone-quarriers have one perch, stone-masons another, etc. Engineers, 
on this account, contract by the ctibic yard. The perch should be done 
away with entirely; perches of 25 cubic feet X 0.926 = cubic yards; and 
cubic yards -i- 0,926 = perches of 25 cubic feet. 



CHAPTER III 



NATURAL SINES, TANGENTS, ETC. 

Sine 

The sine of any angle acb or the sine of any circular arc ab is the 
perpendicular distance, as, from one end of the arc a to the radius 
passing through the other end b of the arc. It 
is equal to one-half the chord of the arc abn, 
which is twice the arc ab; or the chord of the 
arc abn is equal to twice the sine of half the arc, 
or twice the sine oi ab. 

The sine of the angle tcb, if tcb equals 90", is 
equal to the radius of the circle. 



t 


u/ 


w 

c 


/ 


eV 

Vers.' 




c 


n 


s 





Fig. 36. 



Cosine 

The cosine of an arc ab is the distance cs from 
the center of the circle c to the intersection of the 
sine as with the radius cb, and is equal to ya or the sine of the arc ta. 
But the angle tea is equal to the difference between 90° and the angle 
acb; or the difference between the arcs tab and ab; and is the comple- 
ment of acb. Hence the cosine of an angle or arc is equal to the sine of 
its complement, and vice versa. 

Versed Sine 

The versed sine of an arc is the distance sb from the foot 5 of the sine 
to the arc at b, measured on the radius cb. 

Natural Sines, Tangents, etc. 

The versed sine of an arc ab is equal to the rise of twice the arc; or 
equal to the rise of abn. 

Tangent 

The tangent bw of an arc ab is the perpendicular .distance from the 
radius at one extremity of the arc b to the intersection w of the perpen- 
dicular bw with the prolongation of a radius drawn through the other 
extremity of the arc at a. 

107 



lo8 Mathematical Tables 

The Secant 

The secant of an arc is the distance cw from the center of the arc to 
the intersection of the tangent at w of the prolonged radius ca. 

If the angle tch equals 90 degrees and tea be the complement of achy 
the sine ya of this complement, its versed sine ty, tangent to and secant 
CO become respectively the cosine, coversed sine, cotangent and co- 
secant of the angle ach, and vice versa. 

When the radius ah is equal to unity the corresponding sines, cosines, 
tangents, etc., are called natural sines, cosines, etc.; and the table con- 
taining their lengths for different angles is the table of natural sines, etc. 

The lengths of the sines, etc., for the arcs of any other circle, whose 
radius may be greater or less than i, are found by multiplying the tabu- 
lar values by such radius. 

The following table contains only natural sines, tangents and secants; 
the other lengths may be found for any angle not exceeding 90 degrees 
as follows: 

Cosine = sine of the complement of the given angle. 

Versed sine = i — cosine. 

Coversed sine = i — sine. 

Cotangent = tangent of the complement. 

Cosecant = i divided by natural sine. 

Sine = = — 7 = V (i — cos^). 

cosec cot 



Tangent 



sm _ _i_ 
cos cot 
tan 



Secant = -^ = i?£ = Vb? + tangent^, 

cos sm 



Cosine = V(i — sin^) = — = sine X cotangent = 

tan sec 



Cotangent 



_ cos _ I 
sin tan 
Versed sine = radius — cosine. 
Coversed sine = radius — sine. 



Radius = tangent X cotangent = v sine^ + cosine^. 

The formulae for the solution of the right-angled and the oblique- 
angled triangle are given; for further information the reader is referred 
to works on Trigonometry, 



Solution of Oblique-angled Triangles 



109 



Solution of the Right-angled Triangle 

LetA,B and C be the angles of the triangle and a, h and c the sides 
opposite those angles respectively. 

Then (i) 



«, 


= sine^, a = c sine^. 


<^)! 


= cosine A, h = c cosine A. 


(3)^ 


= tangent A, a = b tangent A 


^^^l 


= cot A, b = a cot A. 



, . Sin ^ 

^^^ C^^ = tangents. 

,,^ Cosyl 

(0). ^^ = cotangent A. 

(7) Sine A + cos^ A = i 



(8) Sine^ = Vi — cosM. 

(9) Cos A = Vi - sind^A. 




Solution of Oblique-angled Triangles 




h 

Fig. 38. 
Value of any side c is: 

a sin C b sin C 



sin^ 



sin 5 



Value of any angle A : 

o sin C a sin B 



Sin^ 
Cos 4 



c b 

b — a cos C c — a cos B 



Tan 4 



C2 ■!■ ^,2 _ ^2 

2 be 
asinC 



a sin 5 



b — aco^C c — acosB' 



no 



Mathematical Tables 



Natural Sines, Tangents and Secants 

Advancing by lo min. 



Deg. 


Min. 


Sine 


Tan- 
gent 


Secant 


Deg. 


Min. 


Sine 


Tan- 
gent 


Secant 





oo 


.0000 


.OCX)0 


I.CX300 




SO 


.IS36 


.1554 


I. 0120 




lO 


.0029 


.0029 


I. 0000 


9 


00 


.1564 


.1584 


I.OI2S 




20 


.0058 


.0058 


I. 0000 




10 


.1593 


.1614 


I. 0129 




30 


.0087 


.0087 


I. 0000 




20 


.1622 


.1644 


I. 0134 




40 


.0116 


.0116 


I. 0001 




30 


.1650 


.1673 


I. 0139 




so 


.0145 


.0145 


I.OCXJI 




40 


.1679 


.1703 


I. 0144 


I ■ 


00 


.0175 


.0175 


1.0002 




SO 


.1708 


.1733 


I. 0149 




10 


.0204 


■ .0204 


1.0002 


10 


00 


.1736 


.1763 


I. 0154 




20 


.0233 


. .0233 


1.0003 




10 


.1765 


.1793 


I. 0160 




30 


.0262 


.0262 


1.0003 




20 


.1794 


.1823 


I. 0165 




40 


.0291 


.0291 


i.Sbo4 




30 


.1822 


.1853 


I. 0170 




50 


.0320 


.0320 


i.ooos 




40 


.1851 


.1883 


I. 0176 


2 


00 


.0349 


.0349 


1.0006 




SO 


.1880 


.1914 


1.0181 




10 


.0378 


.0378 


1.0007 


II 


00 


.1908 


.1944 


I. 0187 




20 


.0407 


.0407 


1.0008 




10 


.1937 


.1974 


I. 0193 




30 


.0436 


.0437 


I. 00 10 




20 


. 1965 


.2004 


1. 0199 




40 


.0465 


.0466 


I.OOII 




30 


.1994 


.2035 


1.0205 




50 


.0494 


.049s 


I. 0012 




40 


.2022 


.2065 


1.0211 


3 


00 


.0523 


.0524 


I. 0014 




SO 


.2051 


.2095 


I. 0217 




10 


.0552 


.0553 


I. 0015 


12 


00 


.2079 


.2126 


1.0223 




20 


.0581 


.0582 


I. 0017 




10 


.2108 


.2156 


1.0230 




30 


.0610 


.0612 


I. 0019 




20 


.2136 


.2186 


1.0236 




40 


.0640 


.0641 


I. 0021 




30 


.2164 


.2217 


1.0243 




50 


.0669 


.0670 


1.0022 




40 


.2193 


.2247 


1.0249 


4 


00 


.0698 


.0699 


1.0024 




SO 


.2221 


.2278 


1.0256 




10 


.0727 


.0729 


1.0027 


13 


00 


.2250 


.2309 


1.0263 




20 


.0756 


.0758 


1.0029 




10 


.2278 


.2339 


1.0270 




30 


.0785 


.0787 


I. 0031 




20 


.2306 


.2370 


1.0277 




40 


.0814 


.0816 


1.0033 




30 


.2334 


.2401 


1.0284 




50 


.0843 


.0846 


1.0036 




40 


.2363 


.2432 


I. 0291 


5 


00 


.0872 


.0875 


1.0038 




SO 


.2391 


.2462 


1.0299 




10 


.0901 


.0904 


I. 0041 


14 


00 


.2419 


.2493 


1.0306 




20 


.0929 


.0934 


1.0043 




10 


.2447 


.2524 


I. 0314 




30 


.0958 


.0963 


1.0046 




20 


.2476 


.2555 


I. 0321 




40 


.0987 


.0992 


1.0049 




30 


.2504 


.2586 


1.0329 




50 


.1016 


.1022 


1.0052 




40 


.2532 


.2617 


1.0337 


6 


00 


.1045 


.1051 


I. 005s 




50 


.2560 


.2648 


1.0345 




10 


.1074 


.1080 


1.0058 


15 


00 


.2588 


.2679 


I.03S3 




20 


.1103 


.1110 


I. 0061 




10 


.2616 


.2711 


I. 0361 




30 


.1132 


.1139 


1.0065 




20 


.2644 


.2742 


1.0369 




40 


.1161 


.1169 


1.0068 




30 


.2672 


.2773 


1.0377 




50 


.1190 


.1198 


1.0072 




40 


.2700 


.2805 


1.0386 


7 


00 


.1219 


.1228 


1.0075 




SO 


.2728 


.2836 


1.0394 




10 


.1248 


.1257 


1.0079 


16 


00 


.2756 


.2867 


1.0403 




20 


.1276 


.1287 


1.0082 




10 


.2784 


.2899 


I. 0412 




30 


.1305 


.1317 


1.0086 




20 


.2812 


.2931 


I. 0421 




40 


.1334 


.1346 


1.0090 




30 


.2840 


.2962 


1.0429 




50 


.1363 


.1376 


1.0094 




40 


.2868 


.2994 


1.0439 


8 


00 


.1392 


.I40S 


1.0098 




SO 


.2896 


.3026 


1.0448 




10 


.1421 


.1435 


I. 0102 


17 


00 


.2924 


.3057 


I.04S7 




20 


.1449 


.1465 


I. 0107 




10 


.2952 


.3089 


1.0466 




30 


.1478 


.1495 


I.OIII 




20 


.2979 


.3121 


1.0476 




40 


.1507 


.1524 


I.0II6 




30 


.3007 


.3153 


1.0485 



Natural Sines, Tangents and Secants iii 

Natural Sines, Tangents and Secants — {Continued) 



Deg. 


Min. 


Sine 


Tan- 
gent 


Secant 


Deg. 


Min. 


Sine 


Tan- 
gent 


Secant 




40 


.3035 


.3185 


1.0495 




SO 


.4514 


.5059 


I . 1207 




SO 


.3062 


.3217 


1.0505 


27 


00 


.4540 


.5095 


I . 1223 


i8 


00 


.3090 


.3249 


I. 0515 




10 


.4566 


.5132 


I . 1240 




10 


.3118 


.3281 


1.0525 




20 


.4592 


.5169 


I. 1257 




20 


.3145 


.3314 


1.0535 




30 


.4617 


.5206 


I. 1274 




30 


.3173 


.3346 


I. 054s 




40 


.4643 


.5243 


1.1291 




40 


.3201 


.3378 


1.0555 




50 


.4669 


.5280 


I . 1308 




50 


.3228 


.3411 


1.0566 


28 


00 


.4695 


.5317 


I . 1326 


19 


00 


.32S6 


.3443 


1.0576 




10 


.4720 


.5354 


I. 1343 




10 


.3283 


.3476 


1.0587 




20 


.4746 


• 5392 


1.1361 




20 


.3311 


.3508 


1.0598 




30 


.4772 


.5430 


I . 1379 




30 


.3338 


.3541 


1.0608 




40 


.4797 


.5467 


I . 1397 




40 


.336s 


.3574 


I. 0619 




SO 


.4823 


.5505 


1.1415 




SO 


.3393 


.3607 


I. 0631 


29 


00 


.4848 


.5543 


I. 1434 


20 


00 


.3420 


.3640 


1.0642 




10 


.4874 


.5581 


I. 1452 




10 


.3448 


.3673 


1.0653 




20 


.4899 


.5619 


1.1471 




20 


.3475 


.3706 


1.0665 




30 


.4924 


.5658 


I. 1490 




30 


.3502 


.3739 


1.0676 




40 


.4950 


.5696 


I. 1509 




40 


.3529 


.3772 


1.0688 




SO 


.4975 


.5735 


I . 1528 




50 


.3SS7 


.3805 


1.0700 


30 


00 


.5000 


.5774 


I. 1547 


21 


00 


.3584 


.3839 


1.0711 




10 


.5025 


.5812 


I . 1566 




10 


.3611 


.3872 


1.0723 




20 


.5050 


.5851 


I. 1586 




20 


.3638 


.3906 


1.0736 




30 


.5075 


.5890 


I . 1606 




30 


.3665 


.3939 


1.0748 




40 


.5100 


.5930 


I . 1626 




40 


.3692 


.3973 


1.0760 




50 


.5125 


.5969 


I . 1646 




SO 


.3719 


.4006 


1.0773 


31 


00 


.5150 


.6009 


I. 1666 


22 


00 


.3746 


.4040 


1.0785 




10 


.5175 


.6048 


I. 1687 




10 


.3773 


.4074 


1.0798 




20 


.5200 


.6088 


I. 1707 




20 


.3800 


.4108 


1.0811 




30 


.5225 


.6128 


I. 1728 




30 


.3827 


.4142 


1.0824 




40 


.5250 


.6168 


I. 1749 




40 


.3854 


.4176 


1.0837 




50 


.5275 


.6208 


I . 1770 




50 


.3881 


.4210 


1.0850 


32 


00 


.5299 


.6249 


I . 1792 


23 


00 


.3907 


.4245 


1.0864 




10 


.5324 


.6289 


1.1813 




10 


.3934 


.4279 


1.0877 




20 


.5348 


.6330 


I. 1835 




20 


.3961 


.4314 


1.0891^ 




30 


.5373 


.6371 


I. 1857 




30 


.3987 


.4348 


1.0904 




40 


.5398 


.6412 


I. 1879 




40 


.4014 


.4383 


I. 0918 




50 


.5422 


.6453 


1.1901 




50 


.4041 


.4417 


1.0932 


33 


00 


.5446 


.6494 


I. 1924 


24 


00 


.4067 


.4452 


1.0946 




10 


.5471 


.6536 


I . 1946 




10 


.4094 


.4487 


I. 0961 




20 


.5495 


.6577 


I. 1969 




20 


.4120 


.4522 


1.0975 




30 


.5519 


.6619 


I. 1992 




30 


.4147 


.4557 


1.0989 




40 


.5544 


.6661 


1.201S 




40 


.4173 


.4592 


I. 1004 




50 


.5568 


.6703 


1.2039 




SO 


.4200 


.4628 


1.1019 


34 


00 


.5592 


.6745 


1.2062 


25 


00 


.4226 


.4663 


I . 1034 




10 


.5616 


.6787 


1.2086 




10 


.4253 


.4699 


I. 1049 




20 


.5640 


.6830 


1.2110 




20 


.4279 


.4734 


I . 1064 




30 


.5664 


.6873 


I. 2134 




30 


.4305 


.4770 


I. 1079 




40 


.5688 


.6916 


I. 2158 




40 


.4331 


.4806 


I. 1095 




SO 


.5712 


.6959 


I. 2183 




50 


.4358 


.4841 


I.IIIO 


35 


00 


.5736 


.7002 


1.2208 


26 


00 


.4384 


.4877 


1.1126 




10 


.5760 


.7046 


I . 2233 




10 


.4410 


.4913 


1.1142 




20 


.5783 


.7089 


1.2258 




20 


.4436 


.4950 


1.1158 




30 


.5807 


.7133 


1.2283 




30 


.4462 


.4986 


1.1174 




40 


.5831 


.7177 


1.2309 




40 


.4488 


.5022 


1.1190 




SO 


.5854 


.7221 


1.233s 



112 



Mathematical Tables 





Natural Sines 


, Tangents 


AND Secants 


— {Continued) 




Deg. 


Min. 


Sine ^ 


ran- 
;ent 


Secant 


Deg. 


Min. 


Sine 


Tan- 
gent 


Secant 


36 


00 


.5878 


7265 


I. 2361 




10 


.7092 


1.0058 


I . 4183 




10 


.5901 


7310 


I . 2387 




20 


.7112 


1.0117 


1.422s 




20 


.5925 


735S 


I. 2413 




30 


.7133 


I. 0176 


1.4267 




30 


.5948 


7400 


1.2440 




40 


.7153 


1.0235 


I. 4310 




40 


.5972 


7445 


1.2467 




50 


.7173 


1.0295 


1.4352 




50 


.5995 


7490 


I . 2494 


46 


00 


.7193 


I.03SS 


1.4396 


37 


00 


.6018 


7536 


I . 2521 




10 


.7214 


I. 0416 


1.4439 




10 


.6041 


7581 


I . 2549 




20 


.7234 


1.0477 


1.4483 




20 


.6065 


7627 


1-2577 




30 


.7254 


1.0538 


1.4527 




30 


.6088 


7673 


1.2605 




40 


.7274 


1.0599 


1.4572 




40 


.6111 


7720 


1.2633 




50 


.7294 


I. 0661 


I. 4617 




50 


.6134 


7766 


I. 2661 


47 


00 


.7314 


1.0724 


1.4663 


38 


00 


.6157 


7813 


I . 2690 




10 


.7333 


1.0786 


1.4709 




10 


.6180 


7860 


I. 2719 




20 


.7353 


1.0850 


1.4755 




20 


.6202 


7907 


1.2748 




30 


.7373 


I. 0913 


1.4802 




30 


.6225 


7954 


1.2778 




40 


.7392 


1.0977 


1.4849 




40 


.6248 


8002 


1.2808 




so 


.7412 


I . 1041 


1.4987 




50 


.6271 


8050 


1.2837 


48 


00 . 


.7431 


1.II06 


1.4945 


39 


00 


.6293 


8098 


1.2868 




10 


.7451 


I.1171 


1.4993 




10 


.6316 


8146 


I . 2898 




20 


.7470 


I . 1237 


1.S042 




20 


.6338 


8195 


1.2929 




30 


.7490 


I. 1303 


1.S092 




30 


.6361 


8243 


I . 2960 




40 


.7509 


I. 1369 


1.5141 




40 


.6383 


8292 


I. 2991 




SO 


.7528 


I. 1436 


1.S192 




50 


.6406 


8342 


1.3022 


49 


00 


.7547 


I . 1504 


1.5243 


40 


00 


.6428 


8391 


I -3054 




10 


.7566 


1.1571 


1.5294 




10 


.6450 


8441 


1.3086 




20 


.7585 


I . 1640 


I . 5345 




20 


.6472 


8491 


1.3118 




30 


.7604 


I . 1708 


1.5398 




30 


.6494 


8541 


1.3151 




40 


.7623 


I. 1778 


I.S450 




40 


.6517 


8591 


I. 3184 




SO 


.7642 


I. 1847 


1.SS04 




SO 


.6539 


8642 


I. 3217 


SO 


00 


.7660 


I.1918 


I. 5557 


41 


00 


.6561 


8693 


1.3250 




10 


.7679 


I. 1988 


1.5611 




10 


.6583 


8744 


1.3284 




20 


.7698 


1.2059 


1.5666 




20 


.6604 


8796 


I. 3318 




30 


.7716 


I.2131 


I. 5721 




30 


.6626 


8847 


1.3352 




40 


.7735 


1.2203 


1.5777 




40 


.6648 


8899 


1.3386 




50 


.7753 


1.2276 


1.5833 




SO 


.6670 


8952 


I. 3421 


51 


00 


.7771 


1.2349 


1.5890 


42 


00 


.6691 


9004 


1.3456 




10 


.7790 


1.2423 


1.5948 




10 


.6713 


9057 


1.3492 




20 


.7808 


1.2497 


1.6005 




20 


.6734 


91 10 


1.3527 




30 


.7826 


I . 2572 


1.6064 




30 


.6756 


9163 


1.3563 




40 


.7844 


I . 2647 


I. 6123 




40 


.6777 


9217 


1.3600 




50 


.7862 


I . 2723 


I. 6183 




50 


.6799 


9271 


1.3636 


52 


00 


.7880 


1.2799 


1.6243 


43 


00 


.6820 


9325 


1.3673 




10 


.7898 


1.2876 


1.6303 




10 


.6841 


9380 


I.3711 




20 


.7916 


1.2954 


1.636s 




20 


.6862 


9435 


1.3748 




30 


.7934 


1.3032 


1.6427 




30 


.6884 


9490 


1.3786 




40 


.7951 


1.1311 


1.6489 




40 


.6905 


9545 


1.3824 




SO 


.7969 


I. 3190 


1.6553 




SO 


.6926 


9601 


1.3863 


S3 


00 


.7986 


1.3270 


I. 6616 


44 


00 


.6947 


9657 


1.3902 




10 


.8004 


I. 3351 


I. 6681 




10 


.6967 


9713 


I. 3941 




20 


.8021 


1.3432 


1.6746 




20 


.6988 


9770 


1.3980 




30 


.8039 


I. 3514 


I. 6812 




30 


.7009 


9827 


I . 4020 




40 


.8056 


1.3597 


1.6878 




40 


.7030 


9884 


I . 4061 




50 


.8073 


1.3680 


1.6945 




50 


.70S0 


9942 


1.4101 


54 


00 


.8090 


1.3764 


I. 7013 


45 


00 


.7071 I 


CXXXJ 


I. 4142 




10 


.8107 


1.3848 


I. 7081 



Natural Sines, Tangents and Secants 



"3 





Natural Sines 


, Tangents 


AND Secants — {Co 


ntinued] 




Deg. 


Min. 


Sine 


ran- 
jent 


Secant 


Deg. 


Min. 


Sine 


Tan- 
gent 


Secant 




20 


.8124 I 


3924 


1.7151 




30 


.8949 


2.0057 


2.2412 




30 


.8141 I 


4019 


I . 7221 




40 


.8962 


2.0204 


2.2543 




40 


.8158 I 


4106 


I. 7291 




SO 


.8975 


2.0353 


2.2677 




SO 


.817s I 


4193 


1.7362 


64 


00 


.8988 


2.0503 


2.2812 


55 


00 


.8192 I 


4281 


1-7434 




10 


.9001 


2.0655 


2.2949 




10 


.8208 I 


4370 


1.7507 




20 


.9013 


2.0809 


2.3088 




20 


.8225 I 


4460 


1.7581 




30 


.9026 


2.0965 


2.3228 




30 


.8241 I 


4550 


1.7655 




40 


.9038 


2.I123 


2.3371 




40 


.8258 I 


4641 


I . 7730 




50 


.9051 


2 . 1283 


2.3515 




50 


.8274 I 


4733 


I . 7806 


6s 


00 


.9063 


2.1445 


2.3662 


S6 


00 


.8290 I 


4826 


1.7883 




10 


.9075 


2.1609 


2.3811 




10 


.8307 I 


4919 


1.7960 




20 


.9088 


2.1775 


2.3961 




20 


.8323 I 


S013 


1.8039 




30 


.9100 


2.1943 


2.4114 




30 


.8339 I 


5108 


1.8118 




40 


.9112 


2.2113 


2.4269 




40 


.835s I 


5204 


I. 8198 




SO 


.9124 


2.2286 


2.4426 




50 


.8371 I 


S30I 


1.8279 


66 


00 


.9135 


2.2460 


2.4586 


57 


00 


.8387 I 


5399 


I. 8361 




10 


.9147 


2.2637 


2.4748 




10 


.8403 I 


5497 


1.8443 




20 


.9159 


2.2817 


2.4912 




20 


.8418 I 


5597 


1.8527 




30 


.9171 


2.2998 


2.5078 




30 


.8434 I 


5697 


I. 8612 




40 


.9182 


2.3183 


2.5247 




40 


.8450 I 


5798 


1.8699 




SO 


.9194 


2.3369 


2.5419 




50 


.8465 I 


5900 


1.8783 


67 


00 


.9205 


2.3559 


2.5593 


58 


00 


.8480 I 


6003 


I. 8871 




10 


.9216 


2.37SO 


2.S570 




10 


.8496 I 


6107 


1.8959 




20 


.9228 


2.3945 


2.5949 




20 


.8511 I 


6213 


1.9048 




30 


.9239 


2.4141 


2.6131 




30 


.8S26 I 


6319 


I. 9139 




40 


.9250 


2.4342 


2.6316 




40 


.8542 I 


6426 


1.9230 




50 


.9261 


2.4545 


2.6504 




50 


.8557 I 


6534 


1.9323 


68 


00 


.9272 


2.4751 


2.6695 


59 


00 


.8572 I 


6643 


I. 9416 




10 


.9283 


2.4960 


2.6888 




10 


.8587 I 


6753 


1.9511 




20 


.9293 


2.S172 


2.708s 




20 


.8601 I 


6864 


1.9606 




30 


.9304 


2.5386 


2.7285 




30 


.8616 I 


6977 


1.9703 




40 


.931S 


2.5605 


2.7488 




40 


.8631 I 


7090 


I . 9801 




SO 


.9325 


2.5826 


2.7695 




50 


.8646 I 


7205 


i.99<io. 


69 


00 


.9336 


2.6051 


2.7904 


6o 


00 


.8660 I 


7321 


2.0000 




10 


.9346 


2.6279 


2.8117 




10 


.8675 I 


7437 


2.0101 




20 


.9356 


2.6511 


2.8334 




20 


.8689 I 


7556 


2.0204 




30 


.9367 


2.6746 


2.8S55 




30 


.8704 I 


767s 


2.0308 




40 


.9377 


2.6985 


2.8779 




40 


.8718 I 


7796 


2.0413 




SO 


.9387 


2.7228 


2.9006 




SO 


.8732 I 


7917 


2.0S19 


70 


00 


.9397 


2.7475 


2.9238 


6i 


00 


.8746 I 


8040 


2.0627 




10 


.9407 


2.772s 


2.9474 




10 


.8760 I 


8165 


2.0736 




20 


.9417 


2.7980 


2.9713 




20 


.8774 I 


8291 


2.0846 




30 


.9426 


2.8239 


2.9957 




30 


.8788 I 


8418 


2.0957 




40 


.9436 


2.8502 


3.0206 




40 


.8802 I 


8546 


2 . 1070 




SO 


.9446 


2.8770 


3.0458 




SO 


.8816 I 


8676 


2.118s 


71 


00 


-9455 


2.9042 


3.0716 


62 


00 


.8829 I 


8807 


2.1301 




10 


.9465 


2.9319 


3.0977 




10 


.8843 I 


8940 


2.1418 




20 


.9474 


2.9600 


3.1244 




20 


.8857 I 


9074 


2.1537 




30 


.9483 


2.9887 


3.1515 




30 


.8870 I 


9210 


2.i6S7 




40 


.9492 


3.0178 


3.1792 




40 


.8884 I 


9347 


2.1786 




SO 


.9502 


3.047s 


3.2074 




50 


.8897 I 


9486 


2.1902 


72 


00 


.9511 


3.0777 


3.2361 


63 


GO 


.8910 I 


9626 


2.2027 




10 


.9520 


3.1084 


3.2653 




10 


.8923 I 


9768 


2.2153 




20 


.9528 


3.1397 


3.2951 




20 


.8936 I 


9912 


2.2282 




30 


.9537 


3.1716 


3.3255 



114 Mathematical Tables 

Natural Sines, Tangents and Secants — (Continiied) 



Deg. 


Min. 


Sine 


Tan- 
gent 


Secant 


Deg. 


Min. 


Sine 


Tan- 
gent 


Secant 




4o 


.9546 


3.2041 


3.3565 




30 


.9890 


6.6912 


6.76SS 




SO 


.9SSS 


3.2371 


3.3881 




40 


.9894 


6.8269 


6.8998 


73 


oo 


.9563 


3.2709 


3.4203 




50 


.9899 


6.9682 


7.0396 




lO 


9S72 


3.3052 


3.4532 


82 


00 


.9903 


7.1154 


7.1853 




20 


9580 


3.3402 


3.4867 




10 


.9907 


7.2687 


7.3372 




30 


9588 


3.3759 


3.5209 




20 


9911 


7.4287 


7-4957 




40 


9596 


3.4124 


3.5559 




30 


9914 


7-5958 


7.6613 




so 


960s 


3.4495 


3.5915 




40 


9918 


7.7704 


7.8344 


74 


c» 


9613 


3.4874 


3.6280 




50 


9922 


7-9S30 


8.0156 




10 


9621 


3.5261 


3.6652 


83 


00 


9925 


8-1443 


8.20S5 




20 


9628 


3.5656 


3.7032 




10 


9929 


8.3450 


8-4047 




30 


9636 


3.6059 


3.7420 




20 


9932 


8.5555 


8.6138 




40 


9644 


3.6470 


3 7817 




30 


9936 


8.7769 


8.8337 




50 


9652 


3.6891 


3.8222 




40 


9939 


9-0098 


9-0652 


75 


CX) 


9659 


3-7321 


3.8637 




50 


9942 


9-2553 


9-3092 




10 


9667 


3.7760 


3.9061 


84 


00 


9945 


9.5144 


9-5668 




20 


9674 


3.8208 


3.9495 




10 


9948 


9.7882 


9-8391 




30 


9681 


3.8667 


3.9939 




20 


9951 


10.0780 


10.1275 




40 


9689 


3.9136 


4.0394 




30 


9954 


10.3854 


10.4334 




so 


9696 


3.9617 


4.0859 




40 


9957 


10.7119 


10.758S 


76 


00 


9703 


4.0108 


4.1336 




so 


9959 


11.0594 


II. 1045 




10 


9710 


4.0611 


4- 1824 


85 


00 


9962 


11.430 


11-474 




20 


9717 


4.1126 


4-2324 




10 


9964 


11.826 


11.868 




30 


9724 


4.1653 


4.2837 




20 


9967 


12.251 


12.291 




40 


9730 


4.2193 


4.3362 




30 


9969 


12.706 


12.745 




so 


9737 


4-2747 


4.3901 




40 


9971 


13.197 


13.23s 


77 


00 


9744 


4.3315 


4.4454 




SO 


9974 


13-727 


13-763 




10 


9750 


4.3897 


4.5022 


86 


00 


9976 


14-301 


14-336 




20 


97S7 


4.4494 


4.5604 




10 


9978 


14-924 


14.958 




30 


9763 


4.S107 


4.6202 




20 


9980 


15-605 


15.637 




40 


9769 


4.5736 


4.6817 




30 


9981 


16.350 


16.380 




SO 


9775 


4.6382 


4.7448 




40 


9983 


17.169 


17.198 


78 


00 


9781 


4.7046 


4.8097 




50 


998s 


18.075 


18.103 




10 


9787 


4.7729 


4.8765 


87 


00 


9986 


19.081 


19.107 




20 


9793 


4.8430 


4. 9452 




10 


9988 


20 . 206 


20.230 




30 


9799 


4.9152 


5.0159 




20 


9989 


21.470 


21.494 




40 


980s 


4.9894 


5.0886 




30 


9990 


22.904 


22.926 




SO 


981 1 


5.0658 


5 . 1636 




40 


9992 


24.542 


24.562 


79 


00 


9816 


5.1446 


5. 2408 




50 


9993 


26.432 


26.451 




10 


9822 


5.2257 


5. 3205 


88 


00 


9994 


28.636 


28.654 




20 


9827 


5. 3093 


5. 4026 




10 


9995 


31.242 


31.258 




30 


9833 


5.3955 


5.4874 




20 


9996 


34.368 


34.382 




40 


9838 


5.4845 


5.5749 




30 


9997 


38.188 


38.202 




SO 


9843 


5.5764 


5.6653 




40 


9997 


42.964 


42.976 


8o 


00 


9848 


5. 6713 


5. 7588 




50 


9998 


49.104 


49.114 




10 


9853 


5. 7694 


5.8554 


89 


00 


9998 


57.290 


57.299 




20 


9858 


S.8708 


5.9554 




10 


9999 


68.750 


68.757 




30 


9863 


5.9758 


5. 0589 




20 


9999 


85.940 


85.946 




40 


9868 


6.0844 


6.1661 




30 I 


0000 


114.589 


I 14. 593 




SO 


9872 


6.1970 


6.2772 




40 I 


0000 


171.885 


171.888 


8i 


00 


9877 


6.3138 


6.3925 




SO I 


0000 


343.774 


343.775 




10 


9881 


6.4348 


6.5121 


90 


00 I 


0000 


Infi- 


Infi- 




20 


9886 


6.5606 


6.6363 








nite 


nite 



Approximate Measurement of Angles / 



115 



Approximate Measurement of Angles 
(i) The four fingers of the hand, held at right angles to the arm 
and at arm's length from the eye, cover about 7 degrees; and an angle 
of 7 degrees corresponds to about 12.2 feet in 100 feet; or to 36.6 feet in 
100 yards; or to 645 feet in a mile. 

(2) By means of a two-foot rule, either on a drawing or between 
distant objects in the field. If the inner edges of a common two-foot 
rule be opened to the extent shown in the column of inches, they will be 
incHned to each other at the angles shown in the column of angles. 
Since an opening of H inch (up to 19 inches or about 105 degrees) corre- 
sponds to from about ]'i degree to i degree, no great accuracy is to be 
expected, and beyond 105 degrees still less, for the liability to error then 
increases very rapidly as the opening becomes greater. Thus, the last 
J-i inch corresponds to about 1 2 degrees. 

Angles for openings intermediate of those given may be calculated to 
the nearest minute or two, by simple proportion, up to 23 in'^hes of 
opening, or about 147 degrees. 



Table of Angles Corresponding to Openings oe a 2-foot 
Rule. (Original.) Trautwine. 



Ins. 


Deg. 


Min. 


Ins. 


Deg. 


Min. 


Ins. 


Deg. 


Min. 


Ins. 


Deg. 


Min. 


H 


I 


12 


3'A 


16 


46 


mi 


32 


40 


10 


49 


15 




I 


48 




17 


22 




33 


17 




49 


54 


H 


2 


24 


H 


17 


59 


7 


33 


54 


Yi 


50 


34 




3 


00 




18 


35 




34 


33 




51 


13 


% 


3 


36 


4 


19 


12 


Yi 


35 


10 


Y2 


51 


53 




4 


II 




19 


48 




35 


47 




52 


33 


I 


4 


47 


H 


20 


24 


¥1 


36 


25 


% 


53 


13 




5 


23 




21 






37 


3 




53 


53 


H 


5 


58 


V2 


21 


37 


% 


37 


41 


II 


54 


34 




6 


34 




22 


13 




38 


19 




55 


14 


H 


7 


10 


% 


22 


50 


8 


38 


57 


H 


55 


55 




7 


46 


> 


23 


27 




39 


35 




56 


35 


H 


8 


22 


5 


24 


3 


1/4 


40 


13 


H 


57 


16 




8 


58 




24 


39 




40 


51 




57 


57 


2 


9 


34 


H 


25 


16 


¥2 


41 


29 


H 


58 


38 




10 


10 




25 


53 




42 


7 




59 


19 


H 


10 


46 


H 


26 


30 


% 


42 


46 


12 


60 


00 




II 


22 




27 


7 




43 


24 




60 


41 


H 


II 


58 


% 


27 


44 


9 


44 


3 


H 


61 


23 




12 


34 




28 


21 




44 


42 




62 


5 


H 


13 


10 


6 


28 


58 


Vi 


45 


21 


Y2 


62 


47 




13 


46 




29 


35 




45 


59 




63 


28 


3 


14 


22 


M 


30 


II 


V2 


46 


38 


H 


64 


II 




14 


58 




30 


49 




47 


17 




64 


53 


H 


15 


34 


M 


31 


26 


% 


47 


56 


13 


65 


35 




16 


10 




32 


3 




48 


35 




66 


18 



ii6 



Mathematical Tables, 



Tables of Angles Corresponding to Openings of a 2-foot 
Rule — {Continued) 



Ins. 


Deg. 


Min. 


Ins. 


Deg. 


Min. 


Ins.. 


Deg. 


Min.- 


Ins. 


Deg. 


Min. 


13M 


67 


I 


16 


83 


37 


1834 


102 


45 


21H 


127 


14 




67 


44 




84 


26 




103 


43 




128 


35 


H 


68 


28 


H 


85 


14 


19 


104 


41 


H 


129 


59 




69 


12 




86 


3 




los 


40 




131 


25 


% 


69 


55 


K2 


86 


52 


34 


106 


39 


22 


132 


53 




70 


38 




87 


41 




107 


40 




134 


24 


14 


71 


22 


% 


88 


31 


Vi 


108 


41 


H 


135 


58 




72 


6 




89 


21 




109 


43 




137 


35 


% 


72 


51 


17 


90 


12 


% 


no 


46 


^A 


139 


16 




73 


36 




91 


3 




III 


49 




141 


I 


yi 


74 


21 


H 


91 


54 


20 


112 


53 


H 


142 


51 




75 


6 




92 


46 




113 


58 




144 


46 


% 


75 


51 


i'^ 


93 


38 


Vi 


115 


5 


23 


146 


48 




76 


36 




94 


31 




116 


12 




148 


58 


15 


77 


22 


% 


95 


24 


V2 


117 


20 


H 


151 


17 




78 


8 




96 


17 




118 


30 




153 


48 


H 


78 


54 


18 


97 


II 


H 


119 


40 


H 


156 


34 




79 


40 




98 


5 




120 


52 




159 


43 


\^ 


80 


27 


H 


99 


00 


21 


122 


6 


% 


163 


27 




81 


14 




99 


55 




123 


20 




168 


18 


% 


82 


2 


^/^ 


100 


51 


H 


124 


36 


24 


180 


00 




82 


49 




lOI 


48 




125 


54 









(3) With the same table, using feet instead of inches. — 

From any point measure 1 2 feet -toward* each object and place marks. 
Measure the distance in feet between these marks. Suppose the first 
column in the table to be feet instead of inches. Then opposite the 
distance in feet will be the angle. 

Vs foot =1.5 inches. 



1 in. = .083 ft. 

2 ins. = .167 ft. 

3 ins. = .25 ft. 



4 ins. = .333 ft. 

5 ins. = .416 ft. 

6 ins. = .5 ft. 



7 ins. = .583 ft. 

8 ins. = .667 ft. 

9 ins. = .75 ft. 



10 ins. = .833 ft. 

11 ins. = .917 ft. 

12 ins. = i.o ft. 



(4) Or, measure toward* each object 100 or any other number 
of feet and place marks. Measure the distance in f.eet between the 
marks. Then 

Sine of half _ • half the distance between the marks 

the angle the distance measured toward one of the objects * 

Find this sine in the table, etc.; take out the corresponding angle and 
multiply it by 2. 



If it is inconvenient to measure toward the objects, measure directly from them. 



Tapers per Foot and Corresponding Angles 



117 



Tapers per Foot and Corresponding Angles 

Computed by E. M. Willson 



Taper 
per 
foot 


Included 


Angle with 


Taper 


Included 


Angle with 


angle 


center line 


per 
foot 


angle 


center line 




Deg. Min. Sec. 


Deg. Min. Sec. 




Deg. Min. Sec. 


Deg. Min. Sec. 


1/64 


4 28 


2 14 


23/^ 


II 18 10 


5 39 5 


H2 


8 58 


4 29 


2/2 


II 53 36 


5 56 48 


Me 


17 54 


8 57 


2% 


12 29 2 


6 14 31 


?i2 


26 52 


13 26 


2% 


13 4 24 


6 32 12 


^i 


35 48 


17 54 


2A 


13 39 42 


6 49 51 


^A2 


44 44 


22 22 


3 


14 15 


7 7 30 


Me 


53 44 


26 52 


3H 


14 SO 14 


7 25 7 


%2 


I 2 34 


31 17 


3H 


15 25 24 


7 42 42 


M 


I II 36 


35 48 


33/i 


16 34 


8 17 


%2 


I 20 30 


40 15 


3I/2 


16 35 40 


8 17 50 


5/16 


I 29 30 


44 45 


3H 


17 10 40 


8 35 20 


1^2 


I 38 22 


49 II 


33/ 


17 45 40 


8 52 50 


H 


I 47 24 


53 42 


3A 


18 20 34 


9 10 17 


m2 


I 56 24 


58 12 


4 


18 55 28 


9 27 44 


Vie 


2 5 18 


I 2 39 


4Vs 


19 30 18 


9 45 9 


m2 


2 14 16 


I 7 8 


4I/4 


20 5 2 


10 2 31 


}i 


2 23 10 


I II 35 


43/^ 


20 39 44 


10 19 52 


m2 


2 32 4 


I 16 2 


4I/2 


21 14 2 


10 37 I 


rie 


2 41 4 


I 20 32 


4H 


21 48 54 


10 54 27 


l?i2 


2 50 2 


I 25 I 


43/ 


22 23 22 


II II 41 


^A 


2 59 42 


I 29 51 


4/8 


22 57 48 


II 28 54 


m2 


3 7 56 


I 33 58 


5 


23 32 12 


II 46 6 


ii/e 


3 16 54 


I 38 27 


5% 


24 6 28 


12 3 14 


m2 


3 25 50 


I 42 55 


5I/4 


24 40 42 


12 20 21 


H 


3 34 44 


I 47 22 


5% 


25 14 48 


12 37 24 


25/^2 


3 43 44 


I 51 52 


5I/2 


25 48 48 


12 54 24 


13/16 


3 52 38 


I 56 19 


sH 


26 22 52 


13 II 26 


2^32 


4 I 36 


2 48 


53/ 


26 56 46 


13 28 23 


li 


4 10 32 


2 5 16 


5% 


27 30 34 


13 45 17 


2%2 


4 19 34 


2 9 47 


6 


28 4 2 


14 2 I 


1^6 


4 28 24 


2 14 12 


6/8 


28 37 58 


14 18 59 


31/^2 


4 37 20 


2 18 40 


61/ 


29 II 34 


14 35 47 


I 


4 46 18 


2 23 9 


63/^ 


29 45 18 


14 52 39 


iHe 


5 4 12 


2 32 6 


6/2 


30 18 26 


15 9 13 


iH 


5 21 44 


2 40 52 


6H 


30 51 48 


IS 25 54 


iMe 


5 39 54 


2 49 57 


63/ 


31 25 2 


15 42 31 


iH 


5 57 48 


2 58 54 


6% 


31 58 10 


IS 59 5 


iMe 


6 15 38 


3 7 49 


7 


32 31 12 


16 IS 36 


l3/i 


6 33 26 


3 16 43 


7% 


33 4 8 


16 32 4 


1^6 


6 51 20 


3 25 40 


7/4 


33 36 40 


16 48 20 


iH 


7 9 10 


3 34 35 


73/^ 


34 9 50 


17 4 55 


I?'! 6 


7 26 58 


3 43 29 


71/2 


34 42 30 


17 21 15 


154 


7 44 48 


3 52 24 


7% 


35 15 2 


17 37 31 


iiMe 


8 2 38 


4 I 19 


7% 


35 47 32 


17 53 46 


iH 


8 20 26 


4 10 13 


7A 


36 19 54 


18 9 57 


113/6 


8 38 16 


4 19 8 


8 


36 52 12 


18 26 6 


1% 


8 56 2 


4 28 I 


8/8 


37 24 22 


18 42 II 


I15/6 


9 13 50 


4 36 55 


m 


37 56 26 


18 58 13 


2 


9 31 36 


4 45 48 


m 


38 28 16 


19 14 8 


2H 


10 7 io 


5 3 35 


81/^ 


39 16 


19 30 8 


2H 


10 42 42 


5 21 21 


85,^ 


39 31 52 


19 45 56 



Ii8 Mathematical Tables, 

Tapers per Foot and Corresponding Angles — (Continued) 



Taper 


Included 


Angle with 


Taper 


Included 


Angle with 


per 
foot 


angle 


center line 


per 
foot 


angle 


center line 




Deg. Min. Sec. 


Deg. Min. Sec. 




Deg. Min. Sec. 


Deg. Min. Sec. 


83/4 


4o 3 42 


20 I SI 


I03/i 


46 45 24 


23 22 42 


8Ji 


4o 35 i6 


20 17 38 


10I/2 


47 15 32 


23 37 46 


9 


41 6 44 


20 33 22 


I05/i 


47 45 30 


23 52 45 


9H 


41 38 28 


20 49 14 


I03^ 


48 15 24 


24 7 42 


9H 


42 9 i8 


21 4 39 


loji 


48 45 10 


24 22 35 


9H 


42 40 26 


21 20 13 


II 


49 14 48 


24 37 24 


9H 


43 II 24 . 


21 35 42 


I1I4 


49 44 20 


24 52 10 


9% 


43 42 20 


21 51 10 


iiH 


50 13 46 


25 6 53 


9% 


44 13 6 


22 6 33 


ii^i 


50 43 4 


25 21 32 


9^ 


44 43 48 


22 21 54 


iiJ-^ 


51 12 14 


25 36 7 


lo 


45 14 22 


22 37 II 


ii^i 


51 41 18 


25 SO 39 


loi^ 


45 44 52 


22 52 26 


iiH 


52 10 16 


26 5 8 


loH 


46 15 46 


23 7 53 


im 


52 39 2 


26 19 31 



CHAPTER IV 



DIFFERENT STANDARDS FOR WIRE GAUGES 



Different Standards for Wire Gauges in Use in the 
United States 

Dimensions of sizes in decimal parts of an inch 



II 

^ .tl 


H., S. & Co. 
"F.&G." 

steel music 
wire gauge 


1 


U.S. 
standard 
for plate 


American or 

Brown & 

Sharpe 


all 


t4 

las 

03 <U P 




1 


OS 

II 


oooooo 






.46875 








.464 




oooooo 


ooooo 






.4375 








.432 




ooooo 


OGOO 






.40625 


.46 


.454 


.3938 


.400 




0000 


coo 






• 375 


.40964 


.42s 


.3625 


.372 




000 


oo 


.0087 




.34375 


.3648 


.38 


.3310 


.348 




00 


o 


.0093 


.0578 


.312s 


.32486 


.34 


.3065 


.324 







I 


.0098 


.0710 


.28125 


.2893 


.3 


.2830 


.300 


.227 


I 


2 


.0106 


.0842 


.265625 


.25763 


.284 


.2625 


.276 


.219 


2 


3 


.0114 


.0973 


.25 


.22942 


.259 


.2437 


.252 


.212 


3 


4 


.0122 


.1105 


.234375 


. 20431 


.238 


.2253 


.232 


.207 


4 


5 


.0138 


.1236 


.21875 


.18194 


.22 


.2070 


.212 


.204 


5 


6 


.0157 


.1368 


.203125 


. 16202 


.203 


.1920 


.192 


.201 


6 


7 


.0177 


.1500 


.1875 


.14428 


.18 


.1770 


.176 


.199 


7 


8 


.0197 


.1631 


.171875 


.12^49 


.165 


.1620 


.160 


.197 


8 


9 


.0216 


.1763 


. 15625 


.11443 


.148 


.1483 


.144 


.194 


9 


ID 


.0236 


.1894 


. 14062s 


. 10189 


.134 


.1350 


.128 


.191 


10 


II 


.0260 


.2026 


.125 


.090742 


.12 


.1205 


.116 


.188 


II 


12 


.0283 


.2158 


.109375 


.080808 


.109 


.1055 


.104 


.185 


12 


13 


.0303 


.2289 


.09375 


.071961 


.09s 


.0915 


.092 


.182 


13 


14 


.0323 


.2421 


.078125 


.064084 


.083 


.0800 


.080 


.180 


14 


IS 


.0342 


.2552 


.0703125 


.057068 


.072 


.0720 


.072 


.178 


IS 


i6 


.0362 


.2684 


.0625 


.05082 


.06s 


.0625 


.064 


.175 


16 


17 


.0382 


.2816 


.05625 


.045257 


.058 


.0540 


.056 


.172 


17 


i8 


.04 


.2947 


.05 


.040303 


.049 


.0475 


.048 


.168 


18 


19 


.042 




.04375 


.03589 


.042 


.0410 


.040 


.164 


19 


20 


.044 


.3210 


.0375 


.031961 


.035 


.0348 


.036 


.161 


20 


21 


.046 




.034375 


.028462 


.032 


.03175 


.032 


.157 


21 


22 


.048 


.3474 


.03125 


.025347 


.028 


.0286 


.028 


.155 


22 


23 


.051 




.028125 


.022571 


.02s 


.0258 


.024 


.153 


23 


24 


• OSS 


3737 


.025 


.0201 


.022 


.0230 


.022 


.151 


24 


25 


.059 




.021875 


.0179 


.02 


.0204 


.020 


.148 


25 


26 


.063 


.4000 


.01875 


.01594 


.018 


.0181 


.018 


.146 


26 


27 


.067 




.0171875 


.014195 


.016 


.0173 


.0164 


.143 


27 


28 


.071 


.4263 


.015625 


.012641 


.014 


.0162 


.0149 


.139 


28 



119 



I20 



Materials 



Deffeeent Standards for Wire Gauges in Use in the 
United States — {Continued) 





&Co. 

music 
gauge 




. S. 

dard 

plate 




1:1 -tt 




2J 


1 


OS, 

u 3 


'1 






^sa 


1" 












29 


.074 




.0140625 


.011257 


.013 


.0150 


.0136 


.134 


29 


30 


.078 


•452 


3 OI2S 


.010025 




012 


.0141 


.0124 


.127 


30 


31 


.082 




•0109375 


.008928 




01 


.0132 


.0116 


.120 


31 


32 


.086 




.01015625 


.00795 




009 


.0128 


.0108 


.115 


32 


33 






- .009375 


.00708 




008 


.0118 


.0100 


.112 


33 


34 






.00859375 


.006304 




007 


.0104 


.0092 


.110 


34 


35 






.0078125 


.005614 




005 


.0095 


.0084 


.108 


35 


36 






.00703125 


.005 




004 


.0090 


.0076 


.106 


36 


37 






.006640625 


.004453 








.0068 


.103 


37 


38 






.00625 


.003965 








.0060 


.101 


38 


39 








.003531 








.0052 


.099 


39 


40 








.003144 








.0048 


.097 


40 



Birmingham Gauge for Sheet Brass, Silver, Gold and all 
Metals except Steel and Iron 





Thick- 




Thick- 




Thick- 




Thick- 




Thick- 




Thick- 


No. 


ness, 


No. 


ness, 


No. 


ness, 


No. 


ness, 


No. 


ness, 


No. 


ness, 




inch 




inch 


13 


inch 




inch 




inch 




inch 


I 


.004 


7 


.015 


.036 


19 


.064 


25 


.095 


31 


.133 


2 


.005 


8 


.016 


14 


.041 


20 


.067 


26 


.103 


32 


.143 


3 


.008 


9 


.019 


15 


.047 


21 


.072 


27 


.113 


33 


.145 


4 


.010 


10 


.024 


16 


.051 


22 


.074 


28 


.120 


34 


.148 


5 


.012 


II 


.029 


19 


.057 


23 


.077 


29 


.124 


35 


.158 


6 


.013 


12 


.034 


18 


.061 


24 


.082 


30 


.126 


36 


.167 



^ Gauges Generally used by Mills in the U. S. Rolling Sheet 
Iron. (Vary Slightly from Birmingham Gauge) 



No. 


Pounds per 


No. 


Pounds per 


No. 


Pounds per 


No. 


Pounds per 


square foot 


square foot 


square foot 


square foot 


I 


12.50 


8 


6.86 


15 


2.81 


22 


1. 25 


2 


12.00 


9 


6.24 


16 


2.50 


23 


1. 12 


3 


11.00 


10 


5.62 


17 


2.18 


24 


1. 00 


4 


10.00 


II 


5.00 


18 


1.86 


25 


.90 


5 


8.75 


12 


4.38 


19 


1.70 


26 


.80 


6 


8.12 


13 


3.75 


20 


1-54 


27 


.72 


7 


7.50 


14 


3.12 


21 


1.40 


28 


.64 



Band and Hoop Iron Weights per Lineal Foot 
Band and Hoop Iron Weights per Lineal Foot 











Width 


in inches 








No. of 




















gauge 






















% 


% 


% 


I 


ii/i 


ii/4 


1% 


m 


1% 




lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


6 


.4231 


.5078 


.5924 


674 


762 


846 


.931 I 


016 


1. 10 


8 


.3581 


.4296 


.5013 


5729 


64s 


716 


.788 


859 


.931 


lo 


.2929 


.3515 


.4101 


4689 


527 


586 


.645 


703 


.762 


II 










469 


521 


.573 


625 


.677 


12 


.2278 


.2734 


.3190 


364s 


41 


456 


.501 


547 


.592 


13 










352 


391 


.430 


469 


.508 


14 


.1628 


.1953 


.2278 


2604 


293 


326 


.358 


391 


.423 


15 










264 


293 


.322 


352 


.381 


i6 


.1302 


.1562 


.1822 


2083 


234 


26 


.286 


313 


.339 


17 


.1139 


.1367 


.1595 


1822 


205 


229 


.251 


273 


.269 


i8 


.0976 


.1171 


.1367 


1562 


176 


195 


.215 


234 


.254 


19 


.0895 


.1074 


.1253 


1432 


161 


179 


.197 


215 




20 


.0814 


.0976 


.1139 


1302 


146 


163 


.179 


195 




21 


■0731 


.0877 


.1023 


1169 . 












22 


.0651 


.0781 


.0911 


104 1 












23 


.0588 


.0705 


.0822 
1 


0939 . 
























Width in inches 










No. of 






















gauge 
























1% 


m 


2 


2}i 


2H 


2% 


2I/2 


2% 


234 


2% 




lbs. 


lbs. 


lbs.' 1 


bs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


4 


1.367 


1.465 


1.562 I 


660 


i.^S8 


1.855 


1.953 


2.051 


2.148 


2.246 


6 


1. 185 


1.270 


1.354 I 


439 


1.523 


1.608 


1.693 


1.777 


1.862 


1-947 


8 


1.003 


1.074 


I . 146 I 


217 


1.289 


1. 361 


1.432 


1.504 


1.576 


1.647 


9 


.914 


.977 


1.042 I 


107 


1. 172 


1.237 


1.302 


1.367 


1.423 


1-497 


10 


.820 


.897 


.938 


996 


1.055 


1. 113 


1. 172 


1. 231 


1.289 


1.348 


II 


.729 


.781 


.833 


88s 


.938 


■990 


1.042 


1.094 


1. 146 


1. 198 


12 


.638 


.684 


.729 


775 


.820 


.866 


.911 


• 957 


1.003 


1.048 


13 


.547 


.586 


.625 


664 


.703 


.742 


.781 


.820 


.859 


.898 


14 


.456 


.488 


.521 


553 


.586 


.618 


.651 


.684 


.716 


.749 


♦ 15 


.410 


.439 


.469 


498 


.527 


.557 


.586 








16 


.36s 


.391 


.417 


443 


.469 


.495 


.521 








17 


.319 


.342 


.365 . 

















18 


.273 


.293 


.313 . 

















22 Materials 

Band and Hoop Iron Weights per Lineal Foot — {Continued) 













Width in inches 










No. of 




















gauge 
























3 


3H 


3H 


3% 


4 


4H 


4H 


5 


SH 


6 




lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


4 


2.344 


2.539 


2.734 


2.930 


3.125 


3.321 


3.516 


3.906 


4.297 


4.688 


5 


2.188 


2.370 


2.552 


2.734 


2.917 


3.099 


3.281 


3.646 


4. on 


4.37s 


6 


2.031 


2.201 


2.370 


2.539 


2.708 


2.878 


3 047 


3.385 


3.724 


4.063 


7 


1.875 


2.031 


2.188 


2.344 


2.500 


2.656 


2.813 


3.125 


3.437 


3 -750 


8 


1. 719 


1.862 


2.005 


2.148 


2.292 


2.435 


2.578 


2.864 


3. 151 


3.438 


9 


1.563 


1.693 


1.823 


1.953 


2.083 


2.214 


2.344 


2.604 


2.865 


3.12s 


lo 


1.406 


1.523 


1. 641 


1.758 


1.875 


1.992 


2.109 


2.344 


2.578 


2.813 


II 


1. 250 


1.354 


1.458 


1.563 


1.667 


1. 771 


1.87s 


2.083 


2.292 


2.500 


13 


1.094 


1. 185 


1.276 


1.367 


1.458 


1.549 


1. 641 


1.823 


2.00S 


2.188 


13 


.938 


1. 016 


1.094 



















14 


.781 


.846 


.911 


















Weights of Flat Rolled Iron per Lineal Foot 



123 



Weights or Flat Rolled Iron per Lineal Foot 

For thicknesses from He inch to 2 inches and widths from i inch to 

12% inches. 

Iron weighing 480 pounds per cubic foot. 



Thick- 


I 


iH 


m 


1% 


2 


2H 


2H 


3% 


12 


ness in 
inches 


inch 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


Ms 


.208 


.260 


.313 


.36s 


.417 


.469 


.521 


.573 


2.50 


H 


.417 


.521 


.625 


.729 


.833 


.938 


1.04 


1. 15 


5.00 


?l6 


.625 


.781 


.938 


1.09 


1.25 


1. 41 


1.56 


1.72 


7.50 


H 


.833 


1.04 


1.25 


1.46 


1.67 


1.88 


2.08 


2.29 


10.00 


Me 


1.04 


1.30 


1.56 


1.82 


2.08 


2.34 


2.60 


2.86 


12.50 


H 


1. 25 


1:56 


1.88 


2.19 


2.50 


2.81 


3.13 


3.44 


I5-00 


Viti 


1.46 


1.82 


2.19 


2.55 


2.92 


3.28 


3.65 


4.01 


17. SO 


H 


1.67 


2.08 


2.50 


2.92 


3.33 


3.75 


4.17 


4.58 


20.00 


%6 


I 88 


2.34 


2.81 


3.28 


3. 75 


4.22 


4.69 


5.16 


22.50 


H 


2.08 


2.60 


3.31 


3.65 


4.17 


4.69 


5.21 


5.73 


25.00 


iMe 


2.29 


2.86 


3-44 


4.01 


4.58 


5.16 


5.73 


6.30 


27.50 


% 


2.50 


3.13 


3.75 


4.38 


500 


5.63 


6.25 


6.88 


30.00 


1^6 


2.71 


3.39 


4.06 


4-74 


5.42 


6.09 


6.77 


7.45 


32.50 


% 


2.92 


3.65 


4.38 


5.10 


5.83 


6.56 


7.29 


8.02 


35.00 


iMe 


3.13 


3.91 


4.69 


5.47 


6.25 


7.03 


7.81 


8.59 


37.50 


I 


3.33 


4.17 


5.00 


5.83 


6.67 


7.50 


8.33 


9.17 


40.00 


iHe 


3.54 


4.43 


5.31 


6.20 


7.08 


7.97 


8.85 


9.74 


42.50 


iH 


3.75 


4.69 


5.63 


6.56 


7.50 


8.44 


9-38 


10.31 


45.00 


iMe 


3.96 


4.95 


5. 94 


6.93 


7-92 


8.91 


9.90 


10.89 


47.50 


iH 


4 17 


5.21 


6.25 


7.29 . 


8.33 


9.38 


10.42 


11.46 


50.00 


1^6 


4.37 


5. 47 


6.56 


7.66 


8.75 


9.84 


10.94 


12.03 


52.50 


l3/6 


4. 58 


5.73 


6.88 


8.02 


917 


10.31 


11.46 


12.60 


55.00 


1M5 


4.79 


5.99 


7.19 


8.39 


958 


10.78 


11.98 


13 18 


57.50 


i3^ 


S.oo 


6.25 


7-So 


8.75 


10.00 


11.25 


12.50 


13-75 


60.00 


iMe 


5. 21 


6.51 


7.81 


9. II 


10.42 


11.72 


13.02 


14.32 


62.50 


i5i 


5.42 


6.77 


8.13 


948 


10.83 


12.19 


13.54 


14.90 


65.00 


iiHe 


5.63 


7-03 


8.44 


9.84 


11.25 


12.66 


14.06 


15.47 


67.50 


zVi 


6.83 


7.29 


8.75 


10.21 


11.67 


13.13 


14.58 


16.04 


70.00 


i^ie 


6.04 


7.5s 


9.06 


10.57 


12.08 


13.59 


15.10 


16.61 


72.50 


1% 


6.25 


7.81 


9.38 


10.94 


12.50 


14.06 


15.63 


17.19 


75 -00 


iiMe 


6.46 


8.07 


9.69 


11.30 


12.92 


14.53 


16. IS 


17.76 


77.50 


2 


6.67 


8.33 


10.00 


11.67 


13-33 


15.00 


16.67 


18.33 


80.00 



124 Materials 

Weights of Flat Rolled Iron per Lineal Foot — {Continued) 



Thick- 


3 


314 


_ 3^2 


._ 3% 


4 


4M 


1 

4V^ 


4% 


12 


ness in 
inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


Me 


.625 


.677 


.729 


.781 


.833 


.885 


.938 


.990' 


2.50 


H 


1.25 


1. 35 


1.46 


1.56 


1.67 


1.77 


1.88 


1.98 


5.00 


He 


1.88 


2.03 


2.19 


2.34 


2.50 


2.66 


2.81 


2.97 


7.50 


H 


2.50 


2.71 


2.92 


3.13 


3.33 


3-54 


3.75 


3.96 


10.00 


Me 


3.13 


3.39 


3.65 


3.91 


4.17 


4.43 


4.69 


4-95 


12.50 


% 


3.75 


4.06 


4.38 


4.69 


S-oo 


5. 31 


5. 63 


5.94 


15.00 


Me 


4.38 


4.74 


S.io 


5.47 


5.83 


6.20 


6.56 


6.93 


17.50 


H 


5.00 


S.42 


5.83 


6.25 


6.67 


7.08 


7.50 


7.92 


20.00 


Vis 


5. 63 


6.09 


6.56 


7.03 


7. So 


7.97 


8.44 


8.91 


22.50 


5/i 


6.25 


6.77 


7.29 


7.81 


8.33 


8.85 


9.38 


9.90 


25.00 


iMe 


6.88 


7-45 


8.02 


8.59 


9.17 


9.74 


10.31 


10.89 


27.50 


% 


7.50 


8.13 


8.75 


9.38 


10.00 


10.63 


11.25 


11.88 


30.00 


me 


8.13 


8.80 


9.48 


10.16 


10.83 


II. SI 


12.19 


12.86 


32.50 


li 


8.75 


9.48 


10.21 


10.94 


11.67 


12.40 


13.13 


13.85 


35.00 


iMe 


9.38 


10,16 


10.94 


11.72 


12.50 


13 .28 


14.06 


14.84 


37.50 


I 


10.00 


10.83 


11.67 


12.50 


13.33 


14.17 


15.00 


15.83 


40.00 


iMa 


10.63 


II. 51 


12.40 


13.28 


14. 17 


15. OS 


15.94 


16.82 


42.50 


i\i 


11.25 


12.19 


13.13 


14.06 


15.00 


IS. 94 


16.88 


17.81 


45.00 


xVie 


11.88 


12.86 


13.85 


14.84 


15.83 


16.82 


17.81 


18.80 


47.50 


iM 


12.50 


13.54 


14.58 


15.63 


16.67 


17.71 


18.75 


19.79 


50.00 


iVie 


13.13 


14.22 


IS. 31 


16.41 


17.50 


18.59 


19.69 


20.78 


52.50 


l3/i 


13.75 


14.90 


16.04 


17.19 


18.33 


19.48 


20.63 


21.77 


55. 00 


iMe 


14.38 


15.57 


16.77 


17.97 


19.17 


20.36 


21.56 


22.76 


57.50 


iH 


15.00 


16.25 


17.50 


18.7s 


20.00 


21.25 


22.50 


23.75 


60.00 


i%e 


IS. 63 


16.93 


18.23 


19.53 


20.83 


22.14 


23.44 


24.74 


62.50 


iH 


16.25 


17.60 


18.96 


20.31 


21.67 


23.02 


24.38 


25.73 


65.00 


iiHe 


16.88 


18.28 


19.69 


21.09 


22.50 


23.91 


25.31 


26.72 


67.50 


1% 


17. SO 


18.96 


20.42 


21.88 


23.33 


24.79 


26.25 


27.71 


70.00 


Il3/i6 


18.13 


19.64 


21.15 


22.66 


24.17 


25.68 


27.19 


28.70 


72.50 


x-'A 


18.75 


20.31 


21.88 


23.44 


25.00 


26.56 


28.13 


29.69 


75. 00 


iiMe 


19.38 


20.99 


22.60 


24.22 


25.83 


27.45 


29.06 


30.68 


77.50 


2 


20.00 


21.67 


23.33 


25.00 


26.67 


28.33 


30.00 


31.67 


80.00 



Weights of Flat Rolled Iron per Lineal Foot 125 

Weights of Flat Rolled Iron per Lineal Foot — {Continued). 



Thick- 


5 


sH 


5\^ 


5% 


6 


6H 


6^2 


m 


12 


ness in 
inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


He 


1.04 


1.09 


1. 15 


1.20 


1.25 


1.30 


1.35 


1. 41 


2.50 


H 


2.08 


2.19 


2.29 


2.40 


2.50 


2.60 


2.71 


2.81 


5-00 


^ie 


3.13 


3.28 


3.44 


3.59 


3.75 


3.91 


4.06 


4.22 


7-50 


Yi 


4.17 


4.38 


4.58 


4.79 


5.00 


5.21 


5.42 


5.63 


10.00 


M6 


5.21 


5.47 


S.73 


S.99 


6.2s 


6.51 


6.77 


7.03 


12.50 


^i 


6.25 


6.56 


6.88 


7.19 


7.50 


7.81 


8.13 


8.44 


15 00 


^6 


7.29 


7.66 


8.02 


8.39 


8.75 


9. II 


948 


9.84 


17-50 


H 


8.33 


8.75 


9.17 


9.58 


10.00 


10.42 


10.83 


11.25 


20.00 


^M 


9- 38 


9.84 


10.31 


10.78 


11.25 


11.72 


12.19 


12.66 


22.50 


H 


10.42 


10.94 


11.46 


11.98 


12.50 


13.02 


13-54 


14.06 


25.00 


1^6 


11.46 


12.03 


12.60 


13.18 


13.75 


14.32 


14.90 


15.47 


27.50 


% 


12.50 


13.13 


13.75 


14-38 


1500 


15.63 


16.25 


16.88 


30.00 


13/i6 


13.54 


14.22 


14.90 


15.57 


16.25 


16.93 


17.60 


18.28 


32.50 


^ 


14.58 


15.31 


16.04 


16.77 


17.50 


18.23 


18.96 


19.69 


35.00 


15/6 


IS. 63 


16.41 


17.19 


17.97 


18.75 


19 53 


20.31 


21.09 


37. so 


I 


16.67 


17.50 


18.33 


19.17 


20.00 


20.83 


21.67 


22.50 


40.00 


iMe 


17.71 


18.59 


19-48 


20.36 


21.25 


22.14 


23.02 


23.91 


42.50 


iH 


18.75 


19.69 


20.63 


21.56 


22.50 


23.44 


24.38 


25. 31 


45.00 


iMe 


19-79 


20.78 


21.77 


22.76 


23.75 


24.74 


25.73 


26.72 


47. SO 


iH 


20.83 


21.88 


22.92 


23.96 


25.00 


26.04 


27.08 


28.13 


50.00 


iMe 


21.88 


22.97 


24.06 


25.16 


26.25 


27.34 


28.44 


29.53 


52.50 


1% 


22.92 


24.06 


25.21 


26.35 


27.50 


28.65 


29.79 


30.94 


55. 00 


l7/i6 


23.96 


25.16 


26.35 


27.55 


28.75 


29.9s 


31.15 


32.34 


57.50 


l^^ 


25.00 


26.25 


27.50 


28.75 


30.00 


31.25 


32.50 


33.75 


60.00 


I9i6 


26.04 


27.34 


28.6s 


29.95 


. 31.25 


32.55 


33.85 


35.16 


62.50 


IH 


27.08 


28.44 


29.79 


31.15 


32.50 


33.85 


35.21 


36.56 


65.00 


liHe 


28.13 


29.53 


30.94 


32.34 


33.75 


35. 16 


36.56 


37.97 


67.50 


iVi 


29.17 


30.63 


32.08 


33.54 


35. 00 


36.46 


37.92 


39.38 


70.00 


Il?i6 


30.21 


31.72 


33.23 


34.74 


36.25 


37.76 


39-27 


40.78 


72.50 


i^i 


31.25 


32.81 


34.38 


35.94 


37.50 


39.06 


40.63 


42.19 


75 -00 


11^6 


32.29 


33.91 


35. 52 


37.14 


38.75 


40.36 


41.98 


43.59 


77 SO 


2 


33.33 


35.00 


36.67 


38.33 


40.00 


41.67 


43.33 


45.00 


80.00 



126 . Materials 

Weights of Flat Rolled Iron per Lineal Foot — (Continued) 



Thick- 


7 


7H 


7H 


7M 


8 


8K 


8^ 


8% 


12 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


Me 


1.46 


1. 51 


I.S6 


1. 61 


1.67 


1.72 


1.77 


1.82 


2.S0 


H 


2.92 


3.02 


3.13 


3.23 


3.33 


3.44 


3.54 


3.65 


S.oo 


Me 


4.38 


4.53 


4.69 


4.84 


5.00 


5.16 


5.31 


5.47 


7.50 


H 


5.83 


6.04 


6.25 


6.46 


6.67 


6.88 


7.08 


7.29 


10.00 


Me 


7.29 


7.55 


7.81 


8.07 


8.33 


8.59 


8.85 


9. II 


12.50 


H 


8.75 


9.06 


9.38 


9.69 


10.00 


10.31 


10.63 


10.94 


15.00 


Me 


10.21 


10.57 


10.94 


11.30 


11.67 


12.03 


12.40 


12.76 


17.50 


H 


11.67 


12.08 


12.50 


12.92 


13.33 


13.75 


14.17 


14^58 


20.00 


Me 


13.13 


13.59 


14.06 


14.53 


15.00 


15.47 


15.94 


16.41 


22.50 


H 


14.58 


15.10 


15.63 


16.15 


16.67 


17.19 


17.71 


18.23 


25.00 


iMe 


16.04 


16.61 


17.19 


17.76 


18.33 


18.91 


19.48 


20.05 


27.50 


% 


17-50 


18.13 


18.75 


19.38 


20.00 


20.63 


21.25 


21.88 


30.00 


iMe 


18.96 


19.64 


20.31 


20.99 


21.67 


22.24 


23.02 


23.70 


32.50 


^i 


20.42 


21.15 


21.88 


22.60 


23.33 


24.06 


24.79 


25.52 


35.00 


iM« 


21.88 


22.66 


23.44 


24.22 


25.00 


25.78 


26.56 


27.34 


37.50 


I 


23.33 


24.17 


25.00 


25.83 


26.67 


27.50 


28.33 


29.17 


40.00 


iMe 


24.79 


25.68 


26.56 


27.45 


28.33 


29.22 


30.10 


30.99 


42.50 


tH 


26.25 


27.19 


28.13 


29.06 


30.00 


30.94 


31.88 


32.81 


45.00 


iMe 


27.71 


28.70 


29.69 


30.68 


31.67 


32.66 


33.65 


34.64 


47.50 


iH 


29.17 


30.21 


31.25 


32.29 


33.33 


34.38 


35.42 


36.46 


SO. 00 


iMe 


30.62 


31.72 


32-81 


33.91 


35-00 


36.09 


37.19 


38.28 


52. so 


m 


32.08 


33.23 


34.38 


35.52 


36.67 


37.81 


38.96 


40.10 


55. 00 


iMe 


33.54 


34-74 


35.94 


37.14 


38.33 


39.53 


40.73 


41.93 


57.50 


I^ 


35.00 


36.25 


37.50 


38.75 


40.00 


41.25 


42.50 


43-75 


60.00 


iMe 


36.46 


37.76 


39-06 


40.36 


41.67 


42.97 


44.27 


45.57 


62. so 


iH 


37.92 


39.27 


40.63 


41.98 


43.33 


44.69 


46.04 


47.40 


65.00 


I»H6 


39.38 


40.78 


42.19 


43.59 


45-00 


46.41 


47-81 


49.22 


67. so 


iM 


40.83 


42.29 


43.75 


45.21 


46.67 


48.13 


49.58 


51.04 


70. CO 


i^Me 


42.29 


43.80 


45.31 


46.82 


48.33 


49.84 


51.35 


52.86 


72. so 


iji 


43.75 


45.31 


46.88 


48.44. 


50.00 


51.56 


53.13 


54.69 


75. 00 


iiMfl 


45.21 


46.82 


48.44 


50.05 


51.67 


53.28 


54.90 


56.51 


77.50 


2 


46.67 


48.33 


50.00 


51.67 


53.33 


55. 00 


56.67 


58.33 


80.00 



Weights of Flat Rolled Iron per Lineal Foot 127 

Weights of Flat Rolled Iron per Lineal Foot — {Continued) 



Thick- 


9 


9^/4 


9H 


9% 


10 


loH 


loj'^ 


1034 


12 


ness in 
inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


He 


1.88 


1.93 


1.98 


2.03 


2.08 


2.14 


2.19 


2.24 


2. so 


\^ 


3.75 


3.85 


3.96 


4.06 


4.17 


4.27 


4.38 


4.48 


S.oo 


3/6 


5.63 


5.78 


5. 94 


6.09 


6.25 


6.41 


6.56 


6.72 


7.50 


M 


7. SO 


7.71 


7.92 


8.13 


8.33 


8.54 


8.7s 


8.96 


10.00 


Me 


9.38 


9-64 


9.90 


10.16 


10.42 


10.68 


10.94 


11.20 


12.50 


?i 


11.25 


11.56 


11.88 


12.19 


12.50 


12.81 


13.13 


13.44 


15.00 


^6 


13.13 


13.49 


13.8s 


14.22 


14.58 


14.95 


15.31 


15.68 


17.50 


\^ 


15.00 


15.42 


15.83 


16.25 


16.67 


17.08 


17.50 


17.92 


20.00 


%6 


16.88 


17.34 


17.81 


18.28 


18.7s 


19.22 


19.69 


20.16 


22.50 


H 


18.75 


19.27 


19.79 


20.31 


20.83 


21.35 


21.88 


22.40 


25.00 


iMe 


20.63 


21.20 


21.77 


22.34 


22.92 


23-49 


24.06 


24.64 


27.50 


% 


22.50 


23.13 


23.75 


24.38 


25.00 


25.62 


26.25 


26.88 


30.00 


13/16 


24.38 


25.05 


25.73 


26.41 


27.08 


27.76 


28.44 


29.11 


32.50 


% 


26.25 


26.98 


27.71 


28.44 


29.17 


29.90 


30.63 


31.3s 


35.00 


1^6 


28.13 


28.91 


29.69 


30.47 


31.2s 


32.03 


32.81 


33.59 


37. SO 


I 


30.00 


30.83 


31.67 


32.50 


33.33 


34.17 


35.00 


35.83 


40.00 


iMe 


31.88 


32.76 


33.65 


34.53 


35.42 


36.30 


37.19 


38.07 


42.50 


1% 


33.75 


34.69 


35.63 


36.56 


37 SO 


38.44 


39-38 


40.31 


45.00 


lYie 


35.63 


36.61 


37.60 


38.59 


39.58 


40.57 


41.56 


42.55 


47.50 


m 


37.50 


38.54 


39-58 


40.63 


41.67 


42.71 


43-75 


44.79 


50.00 


iMe 


39 38 


40.47 


41 56 


42.66. 


43.75 


44.84 


45-94 


47.03 


52.50 


134 


41.25 


42.40 


43.54 


44.69 


45.83 


46.98 


48.13 


49-27 


55. 00 


iMe 


43.13 


44.32 


45.52 


46.72 


47.92 


49.11 


SO. 31 


51-51 


57.50 


1I/2 


45.00 


46.2s 


47-50 


48.7s 


50.00 


51.25 


52.50 


53-75 


60.00 


l9/l6 


46.88 


48.18 


49-48 


so. 78 


52.08 


53.39 


54.69 


55.99 


62.50 


15^ 


48.75 


SO. 10 


SI. 46 


52.81 


54.17 


55.52 


56.88 


58.23 


65.00 


iiMe 


50.63 


52.03 


53-44 


54.84 


56.25 


57.66 


59 -06 


60.47 


67.50 


iH 


52.50 


53.96 


55.42 


56.88 


58.33 


59-79 


61.25 


62.71 


70.00 


mis 


54.38 


55.89 


57.40 


58.91 


60.42 


61.93 


63.44 


64.9s 


72. SO 


1% 


56.25 


57.81 


59-38 


60.94 


62.50 


64.06 


65.63 


67.19 


75. 00 


115/16 


58.13 


59-74 


61.35 


62.97 


64.58 


66.20 


67.81 


69.43 


77.50 


2 


60.00 


61.67 


63.33 


65.00 


66.67 


68.33 


70.00 


71.67 


80.00 



128 Materials 

Weights of Flat Rolled Iron per Lineal Foot — {Continued) 



Thick- 


II 


11% 


iiH 


11% 


12 


12H 


I2l/^ 


1234 


ness in 
inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


He 


2.29 


2.34 


2.40 


2.45 


2.50 


2.55 


2.60 


2.66 


^i 


4.58 


4.69 


4.79 


4.90 


5.00 


5-10 


5-21 


S-31 


Yit 


6.88 


7.03 


7.19 


7-34 


7.50 


7-66 


7.81 


7.97 


H 


917 


9.38 


9.58 


9-79 


10.00 


10.21 


10.42 


10.63 


Me 


11.46 


11.72 


11.98 


12.24 


12.50 


12.76 


13 02 


13.28 


3/i 


13.75 


14.06 


14.38 


14.69 


15.00 


IS- 31 


15-63 


15.94 


Me 


16.04 


16.41 


16.77 


17-14 


17.50 


17-86 


18.23 


18-59 


Yi 


18.33 


18.75 


19.17 


19-58 


20.00 


20.42 


20.83 


21.25 


»/e 


20.63 


21.09 


21.56 * 


21.94 


22.50 


22.97 


23.44 


23-91 


5i 


22.92 


23.44 


23.96 


24.48 


25.00 


25-52 


26.04 


26.56 


iHe 


25.21 


25.78 


26.35 


26.93 


27.50 


28.07 


28.65 


29.22 


H 


27.50 


28.13 


28.75 


29-38 


30.00 


30-63 


31-25 


31.88 


13/(6 


29.79 


30.47 


31.15 


31-82 


32.50 


33.18 


33.85 


34-53 


?i 


32.08 


32-81 


33. 54 


34.27 


3500 


35.73 


36-46 


37.19 


15i6 


34.38 


35-16 


35.94 


36.72 


37.50 


38-28 


39-06 


39-84 


I 


36.67 


37.50 


38.33 


39.17 


40.00 


40.83 


41-67 


42.50 


iHe 


38.96 


39.84 


40.73 


41.61 


42.50 


43-39 


44.27 


45.16 


iH 


41.25 


42.19 


43.13 


44-06 


45.00 


45-94 


46.88 


47-81 


I?i6 


43.54 


44.53 


45-52 


46-51 


47-50 


48.49 


49-48 


50.47 


iH 


45.83 


46.88 


47.92 


48.96 


50.00 


51 04 


52-08 


53-13 


iMe 


48.13 


49.22 


50.31 


51-41 


52-50 


53-59 


54-69 


55. 78 


l3/i 


50.42 


51 56 


52.71 


53.85 


55 00 


56.15 


57-29 


58.44 


1^6 


52.71 


53.91 


55.10 


56.30 


57-50 


58.70 


S9-90 


61.09 


iH 


55.00 


56.25 


57 -50 


58.75 


60.00 


61.25 


62.50 


63.7s 


i?ie 


57.29 


58.59 


5990 


61.20 


62.50 


63.80 


65.10 


66.41 


l5i 


59.98 


60.94 


62.29 


63-65 


65.00 


66.35 


67.71 


69.06 


i^Me 


61.88 


63.28 


64-69 


66.09 


67-50 


68.91 


70.31 


71.72 


l3/i 


64.17 


65.63 


67.08 


68.54 


70.00 


71.46 


72.92 


74.38 


Il3/i6 


66.46 


67.97 


69.48 


70.99 


72.50 


74 -01 


75.52 


77.03 


1% 


68.75 


70.31 


71.88 


73-44 


75.00 


76-56 


78.13 


79.69 


i^Me 


71.04 


72.66 


74.27 


75.89 


77.50 


79-11 


80 73 


82.34 


2 


73.33 


75.00 


76.67 


78.33 


80.00 


81.67 


83.33 


85.00 



The weights for 12-inch width are repeated on each page to facilitate making the 
additions necessary to obtain the weights of plates wider than 12 inches. Thus, to 
find the weight of I5}4"X%", add the weights to be found in the same line for zM X% 
and 12x3^=9.48 + 35.00 = 44.48 pounds. 



Areas of Flat Rolled Iron 



129 



Areas of Flat Rolled Iron 

For thicknesses from Me inch to 2 inches and widths from i inch to 12% inches. 



Thick- 


I 


m 


iH 


m 


2 


21/4 


21/2 


2% 


12 


ness in 
inches 


inch 

■ 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


He 


.063 


.078 


.094 


.109 


.125 


.141 


.156 


.172 


.750 


H 


.125 


.156 


.188 


.219 


.250 


.281 


.313 


.344 


I. SO 


ri6 


.188 


.234 


.281 


.328 


.375 


.422 


.469 


.516 


2.25 


M 


.250 


.313 


.375 


.438 


.500 


.563 


.625 


.688 


• 3.00 


Me 


.313 


.391 


.469 


.547 


.625 


.703 


.781 


.859 


3.7s 


H 


• 375 


' .469 


.563 


.656 


.750 


.844 


.938 


1.03 


4.50 


He 


.438 


.547 


.656 


.766 


.875- 


.984 


1.09 


1.20 


5.25 


H 


.500 


.625 


.750 


.875 


1. 00 


1. 13 


1. 25 


1.38 


6.00 


9/i6 


.563 


.703 


.844 


.984 


1. 13 


X.27 


1. 41 


1.55 


6.75 


% 


.625 


.781 


.938 


1.09 


1.25 


1. 41 


1.56 


1.72 


7.50 


^yie 


.688 


.859 


1.03 


1.20 


1.38 


1.55 


1.72 


1.89 


8.25 


H 


.750 


.938 


1. 13 


1. 31 


1.50 


1.69 


1.88 


2.06 


9.00 


13/ie 


.813 


1.02 


1.22 


1.42 


1.63 


1.83 


2.03 


2.23 


9.75 


li 


.875 


1.09 


1.31 


1.53 


1.75 


1.97 


2.19 


2.41 


10.50 


15/ie 


.938 


1. 17 


1. 41 


1.64 


1.88 


2. II 


2.34 


2.58 


11.25 


I 


1. 00 


1. 25 


1.50 


1.7s 


2.00 


2.25 


2.50 


2.75 


12.00 


iMe 


1.06 


1.33 


1.59 


1.86 


2.13 


2.39 


2.66 


2.92 


12.75 


iH 


1. 13 


1. 41 


1.69 


1.97 


2.25 


2.53 


2.81 


3.09 


13.50 


iHe 


1. 19 


1.48 


1.78 


2.08 


2.38 


2.67 


2.97 


3.27 


14.25 


m 


1.25 


i.S6 


1.88 


2.19- 


2.50 


2.81 


3.13 


3.44 


15 00 


iHe 


1. 31 


1.64 


1.97 


2.30 


2.63 


2.95 


3.28 


3.61 


15.75 


l3/i 


1.38 


1.72 


2.06 


2.41 


2.75 


3.09 


3.44 


3.78 


16.50 


iHe 


1.44 


1.80 


2.16 


2.52 


2.88 


3.23 


3.59 


3.95 


17.25 


iV^ 


I. SO 


1.88 


2.25 


2.63 


3.00 


3.38 


3.75 


4.13 


18.00 


I?i6 


i.S6 


1. 95 


2.34 


2.73 


3.13 


3.52 


3.91 


4.30 


18.75 


iH 


1.63 


2.03 


2.44 


2.84 


3.25 


3.66 


4.06 


4-47 


19 50 


iiHe 


1.69 


2. II 


2.53 


2.9s 


3.38 


3.80 


4.22 


4.64 


20.25 


13/4 


1.75 


2.19 


2.63 


3.06 


3.50 


3.94 


4.38 


4.81 


21.00 


iiHe 


1. 81 


2.27 


2.72 


3.17 


3.63 


4.08 


4.53 


4.98 


21.75 


m 


1.88 


2.34 


2.81 


3.28 


3.75 


4.22 


4.69 


5. 16 


22.50 


iiMe 


1.94 


2.42 


2.91 


3.39 


3.88 


4.36 


4.84 


S.33 


23.25 


2 


2.00 


2.50 


3.00 


3. SO 


4.00 


4.50 


5.00 


S.50 


24.00 



I30 



Materials 



Weights of Flat Rolled Steel per Lineal Foot 

For thicknesses from Vie inch to 2 inches and widths from i inch to 12% inches. 



Thick- 
ness in 
inches 


I 


iH 


1I/2 


lU 


2 


2H 


2H 


2?4 


12 


inch 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


Me 


.638 


.797 


. .957 


I. II 


1.28 


1.44 


1.59 


1.75 


7.65 


H 


.850 


1.06 


1.28 


1.49 


1.70 


1. 91 


2.12 


2.34 


10.20 


Me 


1.06 


1.33 


1-59 


1.86 


2.12 


2.39 


2.65 


2.92 


12.7s 


% 


1.28 


1.59 


1.92 


2.23 


2.55 


2.87 


3.19 


3.51 


15.30 


Me 


1.49 


1.86 


2.23 


2.60 


2.98 


3.35 


3.72 


4.09 


17.85 


H 


1.70 


2.12 


2.55 


2.98 


3.40 


3.83 


4.25 


4.67 


20.40 


Me 


1.92 


2.39 


2.87 


3.35 


3.83 


4-30 


4.78 


5.26 


22.95 


% 


2.12 


2.65 


3.19 


3.72 


4.25 


4.78 


5.31 


5.84 


25 50 


iMe 


2.34 


2.92 


3.51 


4.09 


4.67 


5.26 


5.84 


6.43 


28.0s 


M 


2.55 


3.19 


3.83 


4-47 


5.10 


5.75 


6.38 


7.02 


30.60 


13/(6 


2.76 


3-45 


4.14 


4.84 


5.53 


6.21 


6.90 


7.60 


33. IS 


li 


2.98 


3-72 


4-47 


5.20 


5.95 


6.69 


7.44 


8.18 


35.70 


iMe 


3.19 


3.99 


4.78 


5. 58 


6.38 


7.18 


7.97 


8.77 


38.25 


I 


3-40 


4-25 


5.10 


5.95 


6.80 


7.65 


8.50 


9-35 


40.80 


iMe 


3.61 


4-52 


5-42 


6.32 


7.22 


8.13 


903 


9-93 


43-35 


i^ 


3.83 


4.78 


5-74 


6.70 


7.65 


8.61 


9-57 


10.52 


45-90 


iMe 


4.04 


5.0s 


6.06 


7.07 


8.08 


9.09 


10.10 


II. II 


48.45 


iH 


4-25 


5.31 


6.38 


7-44 


8.50 


9-57 


10.63 


11.69 


51 00 


iMe 


4.46 


5.58 


6.69 


7.81 


8.93 


10.04 


II. 16 


12.27 


53.55 


l3/i 


4.67 


5.84 


7.02 


8.18 


9.35 


10.52 


11.69 


12.85 


56.10 


iMe 


4.89 


6.11 


7-34 


8.56 


9-78 


11.00 


12.22 


13.44 


58.65 


iH 


5.10 


6.38 


7.65 


8.93 


10.20 


11.48 


12.75 


14.03 


61.20 


iMe 


5.32 


6.64 


7.97 


930 


10.63 


11.95 


13.28 


14.61 


63.7s 


i5i 


5-52 


6.90 


8.29 


9.67 


11.05 


12.43 


13.81 


15.19 


66.30 


iii/ie 


5.74 


7.17 


8.61 


10.04 


11.47 


12.91 


14.34 


15.78 


68.8S 


1% 


5.9s 


7.44 


8.93 


10.42 


11.90 


13.40 


14.88 


16.37 


71.40 


Il3/i6 


6.16 


7.70 


9-24 


10.79 


12.33 


13.86 


15.40 


16.95 


73. 95 


i^i 


6.38 


7.97 


9-57 


II. 15 


12.75 


14.34 


15.94 


17.53 


76.50 


iiMe 


6.59 


8.24 


9.88 


11.53 


13.18 


14.83 


16.47 


18.12 


79 05 


2 


6.80 


8.50 


10.20 


11.90 


13.60 


15.30 


17.00 


18.70 


81.60 



Weights of Flat Rolled Steel per Lineal Foot 131 

Weights of Flat Rolled Steel per Lineal Foot — (Continued) 



Thick- 


3 


3H 


3H 


3M 


4 


4H 


4^2 


43/4 


12 


ness in 
inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


M« 


1. 91 


2.07 


2.23 


2-39 


2.55 


2.71 


2.87 


3.03 


7-65 


V* 


2.55 


2.76 


2.98 


3-19 


3-40 


3-61 


3-83 


4.04 


10.20 


Me 


3.19 


3.45 


3-72 


3-99 


4-25 


4-52 


4-78 


5.05 


12.75 


H 


3.83 


4.15 


4-47 


4.78 


5-10 


5-42 


5-74 


6.06 


15-30 


Mo 


4.46 


4.83 


5. 20 


5-58 


5-95 


6.32 


6.70 


7-07 


17.85 


H 


5.10 


5.53 


5-95 


6.38 


6.80 


7.22 


7-65 


8.08 


20.40 


Mo 


5. 74 


6.22 


6.70 


7-17 


7-65 


8.13 


8.61 


9-09 


22.95 


H 


6.38 


6.91 


7-44 


7-97 


8.50 


9-03 


9-57 


10.10 


25.50 


iMo 


7.02 


7.60 


8.18 


8.76 


9-35 


9-93 


10.52 


II. II 


28.05 


H 


7.6s 


8.29 


8.93 


9-57 


10.20 


10.84 


11.48 


12.12 


30.60 


13/6 


8.29 


8.98 


9.67 


10.36 


11.05 


11.74 


12.43 


13-12 


33. IS 


^ 


8.93 


967 


10.41 


II. 16 


11.90 


12.65 


13-39 


14-13 


35-70 


iMe 


957 


10.36 


II. 16 


XI. 95 


12.75 


13-55 


14.34 


15-14 


38-25 


I 


10.20 


11.05 


11.90 


12.75 


13-60 


14-45 


15-30 


16.15 


40.80 


1H6 


10.84 


11.74 


12.65 


13-55 


14-45 


15 -35 


16.26 


17.16 


43-35 


IH 


11.48 


12.43 


13.39 


14-34 


15-30 


16.26 


17.22 


18.17 


45 -90 


IM6 


12.12 


13.12 


14-13 


15 -i4 


16.15 


17.16 


18.17 


19.18 


48.45 


I^ 


12.75 


13-81 


14-87 


15-94 


17.00 


18.06 


19-13 


20.19 


51.00 


iMe 


13.39 


14.50 


15-62 


16.74 


17-85 


18.96 


20.08 


21.20 


53-55 


l3/i 


1403 


15.20 


16.36 


17 -"53 


18.70 


19-87 


21.04 


22.21 


56.10 


iMe 


1466 


15-88 


17.10 


18.33 


19-55 


20.77 


21-99 


23.22 


S8-6S 


iH 


15.30 


16. S8 


17-85 


19.13 


20-40 


21.68 


22.9s 


24.23 


61.20 


1^6 


15-94 


17-27 


18.60 


19-92 


21.25 


22.58 


23-91 


25.24 


63.75 


1% 


16.58 


17-96 


19-34 


20.72 


22.10 


23.48 


24.87 


26.25 


66.30 


iiHe 


17.22 


18.65 


20.08 


21.51 


22.95 


24-38 


25.82 


27.26 


68.85 


1% 


17.85 


19-34 


20.83 


22.32 


23.80 


25-29 


26.78 


28.27 


71.40 


iiMe 


18.49 


20.03 


21.57 


23.11 


24.6s 


26.19 


27.73 


29.27 


73-95 


1% 


19- 13 


20.72 


22.31 


23.91 


25.50 


27.10 


28.69 


30.28 


76 -SO 


iiS/ie 


19.77 


21.41 


23.06 


24-70 


26.3s 


28.00 


29.64 


31-29 


7905 


2 


20.40 


22.10 


23-80 


25 -SO 


27.20 


28.90 


30.60 


32-30 


81.60 



132 Materials 

Weights of Flat Rolled Steel per Lineal Foot -^ {Continued) 



Thick- 


5 


5H 


s'A 


.5% 


6 


6H 


6H 


63/4 


12 


ness in 
inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


3/i6 


3.19 


3.35 


3-51 


3.67 


3.83 


3.99 


4.14 


4-30 


7.6s 


H 


4.25 


4-46 


4-67 


4-89 


5- 10 


5-31 


5.53 


5-74 


10.20 


Me 


5.31 


5-58 


5.84 


6. II 


6.38 


6.64 


6.90 


7-17 


12.75 


H 


6.38 


6.69 


7.02 


7-34 


7.65 


7-97 


8.29 


8.61 


15.30 


Me 


7.44 


7.81 


8.18 


8.56 


8.93 


9-29 


9-67 


10.04 


17.85 


H 


8.S0 


8.93 


9-35 


9-77 


10.20 


10.63 


11-05 


11.48 


20.40 


ri6 


9.57 


10.04 


10.52 


11.00 


11.48 


11-95 


12-43 


12.91 


22.95 


% 


10.63 


II. 16 


11.69 


12.22 


12.75 


13-28 


13-81 


14-34 


25.50 


iHe 


11.69 


12.27 


12.85 


13-44 


14 -03 


14-61 


15 20 


15-78 


28.05 


% 


12.75 


13-39 


14.03 


14.67 


15.30 


15-94 


16.58 


17.22 


30.60 


iMe 


13-81 


14.50 


15.19 


15-88 


16.58 


17.27 


17.95 


18.65 


33. IS 


% 


14.87 


15-62 


16.36 


17.10 


17.85 


18.60 


19-34 


20.08 


35.70 


1^6 


15.94 


16.74 


17-53 


18.33 


19 -13 


19.92 


20.72 


21.51 


38.2s 


I 


17.00 


17-85 


18.70 


19-55 


20.40 


21.25 


22.10 


22.95 


40.80 


iMa 


18.06 


18.96 


19-87 


20.77 


21.68 


22.58 


23-48 


24.39 


43.35 


iH 


19-13 


20.08 


21.04 


21.99 


22.95 


23.91 


24-87 


25.82 


45.90 


iMe 


20.19 


21.20 


22.21 


23-22 


24-23 


25.23 


26.24 


27 25 


48.45 


iH 


21.25 


22.32 


23-38 


24.44 


25-50 


26.56 


27.62 


28.69 


51.00 


iMe 


22.32 


23-43 


24-54 


25.66 


26.78 


27.90 


29.01 


30.12 


53.55 


iH 


23.38 


24-54 


25.71 


26.88 


28.05 


29.22 


30.39 


31.56 


56.10 


I7l6 


24.44 


25-66 


26.88 


28.10 


29.33 


30.55 


31.77 


32.99 


58.65 


ii/^ 


25.50 


26.78 


28.05 


29-33 


30.60 


31.88 


33.15 


34.43 


61.20 


I9i6 


26.57 


27-89 


29.22 


30-55 


31.88 


33.20 


34.53 


35.86 


63.75 


l5/i 


27.63 


29.01 


30-39 


31-77 


33.15 


34.53 


35.91 


37.29 


66.30 


iiMe 


28.69 


30.12 


31.55 


32.99 


34.43 


35.86 


37.30 


38.73 


68.85 


l3/i 


29.75 


31-24 


32.73 


34.22 


35.70 


37.19 


38.68 


40.17 


71.40 


113/16 


30.81 


32.35 


33.89 


35.43 


36.98 


38.52 


40.05 


41.60 


73.95 


1% 


31.87 


33-47 


35.06 


36.65 


38.25 


39.85 


41-44 


43.03 


76.50 


iiMe 


32.94 


34-59 


36.23 


37.88 


39.53 


41.17 


42.82 


44.46 


79.0s 


2 


34.00 


35-70 


37.40 


39-10 


40.80 


42.50 


44-20 


45.90 


81.60 



Weights of Flat Rolled Steel per Lineal Foot 133 

Weights of Flat Rolled Steel per Lineal Foot — {Continmd) 



Thick- 
ness in 
inches 


7 


7H 


7!/^ 


73/ 


8 


8H 


81^ 


8% 


12 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


3/i6 


4.46 


4.62 


4.78 


4.94 


5.10 


5.26 


5. 42 


5. 58 


7.6s 


K4 


5. 95 


6.16 


6.36 


6.58 


6.80 


7.01 


7.22 


7-43 


10.20 


Me 


7.44 


7.70 


7.97 


8.23 


8.50 


8.76 


9.03 


9.29 


12.75 


% 


8.93 


9.25 


9.57 


9.88 


10.20 


10.52 


10.84 


II. 16 


15.30 


Vie 


10.41 


10.78 


II. 16 


11.53 


11.90 


12.27 


12.64 


13.02 


17.8S 


H 


11.90 


12.32 


12 75 


13.18 


13.60 


14.03 


14.44 


14.87 


20.40 


Vie 


13.39 


13.86 


14.34 


14.82 


15.30 


15.78 


16.27 


16.74 


22.95 


% 


14.87 


15.40 


15.94 


16.47 


17.00 


17.53 


18.06 


18.59 


25.50 


iMe 


16.36 


16.94 


17.53 


18.12 


18.70 


19.28 


19.86 


20.45 


28.05 


M 


17.85 


18.49 


19.13 


19.77 


20.40 


21.04 


21.68 


22.32 


30.60 


13/16 


19.34 


20.03 


20.72 


21.41 


22.10 


22.79 


23.48 


24.17 


33. IS 


% 


20.83 


21.57 


22.32 


23.05 


23.80 


24-55 


25.30 


26.04 


35.70 


1^6 


22.32 


23.11 


23.91 


24.70 


25.50 


26.30 


27.10 


27.89 


38.25 


I 


23.80 


24.6s 


25.50 


26.35 


27.20 


28.05 


28.90 


29.75 


40.80 


iHe 


25.29 


26.19 


27.10 


28.00 


28.90 


29.80 


30.70 


31.61 


43-35 


iH 


26.78 


27.73 


28.68 


29.64 


30.60 


31.56 


32.52 


33-47 


45-90 


I3/16 


28.26 


29.27 


30.28 


31.29 


32.30 


33.31 


34.32 


35-33 


48.4s 


i>i 


29.75 


30.81 


31.88 


32.94 


34.00 


35.06 


36.12 


37.20 


SI .00 


I5/16 


31.23 


32.35 


33.48 


34-59 


35.70 


36.81 


37.93 


39 -05 


53.55 


l3/i 


32.72 


33.89 


35.06 


36.23" 


37.40 


38.57 


39-74 


40.91 


56.10 


I7/16 


34.21 


35.44 


36.66 


37.88 


39- 10 


40.32 


41.54 


42.77 


58.6s 


IH 


35.70 


36.98 


38.26 


39.53 


40.80 


42.08 


43-35 


44.63 


61.20 


I?l6 


37.19 


38.51 


39.84 


41.17 


42.50 


43.83 


45-16 


46.49 


63.7s 


i-H 


38.67 


40.05 


41.44 


42.82 


44.20 


45.58 


46.96 


48.34 


66.30 


iiMe 


40.16 


41.59 


43.03 


44.47 


45.90 


47.33 


48.76 


50.20 


68.85 


l3/4 


41-65 


43.14 


44.63 


46.12 


47.60 


49.09 


50.58 


52.07 


71.40 


113/6 


43.14 


44.68 


46.22 


47.76 


49.30 


SO. 84 


52.38 


53.92 


73.95 


1% 


44.63 


46.22 


47.82 


49.40 


5100 


52.60 


54. 20 


55.79 


76.50 


115/6 


46.12 


47.76 


49.41 


51 -OS 


52.70 


54.35 


56.00 


57.64 


79.05 


2 


4760 


49.30 


51 00 


52.70 


54.40 


56.10 


57.80 


59.50 


81.60 



134 Materials 

Weights or Flat Rolled Steel per Lineal Foot — (Continued) 



Thick- 
ness in 
inches 


9 


9M 


9H 


9% 


10 


loH 


loi/^ 


I03/4 


12 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


Me 


5.74 


5.90 


6.06 


6.22 


6.38 


6.54 


6.70 


6.86 


7.6s 


H 


7.65 


7.86 


8.08 


8.29 


8.50 


8.71 


8.92 


9.14 


10.20 


Me 


9.56 


9.83 


10.10 


10.36 


10.62 


10.89 


II. 16 


11.42 


12.75 


% 


11.48 


11.80 


12.12 


12.44 


12.75 


13.07 


13.39 


13. 71 


1S.30 


Vl6 


13.40 


13.76 


14.14 


14.51 


14.88 


15.25 


15.62 


15.99 


17.8S 


H 


15.30 


15.73 


16.16 


16.58 


17.00 


17.42 


17.85 


18.28 


20.40 


Me 


17.22 


17.69 


18.18 


18.65 


19.14 


19.61 


20.08 


20.56 


22.95 


% 


19.13 


19.65 


20.19 


20.72 


21.25 


21.78 


22.32 


22.85 


25.50 


iMe 


21.04 


21.62 


22.21 


22.79 


23.38 


23.96 


24.54 


25.13 


28.0s 


H 


22.96 


23.59 


24.23 


24.86 

■ 


25.50 


26.14 


26.78 


27.42 


30.60 


iMe 


24.86 


25.55 


26.24 


26.94 


27.62 


28.32 


29.00 


29.69 


33.15 


Ti 


26.78 


27.52 


28.26 


29.01 


29.75 


30.50 


31.24 


31.98 


35.70 


15/16 


28.69 


29.49 


30.28 


31.08 


31.88 


32.67 


33.48 


34.28 


38.2s 


I 


30.60 


31.4s 


32.30 


33.15 


34.00 


34.85 


35.70 


36.55 


40.80 


iMe 


32.52 


33.41 


34.32 


35.22 


36.12 


37.03 


37.92 


38.83 


4335 


iH 


34.43 


35.38 


36.34 


37.29 


38.25 


39.21 


40.17 


41.12 


45.90 


iMe 


36.34 


37.35 


38.36 


39.37 


40.38 


41.39 


42.40 


43.40 


48.4s 


iH 


38.26 


39.31 


40.37 


41.44 


42.50 


43.56 


44.63 


45.69 


SI. 00 


iMe 


40.16 


41.28 


42.40 


43.52 


44.64 


45.75 


46.86 


47.97 


53.55 


iH 


42.08 


43.25 


44.41 


45.58 


46.75 


47.92 


4908 


50.25 


56.10 


iMe 


44.00 


45.22 


46.44 


47.66 


48.88 


50.10 


51.32 


52.54 


S8.6S 


iH 


45.90 


47.18 


48.45 


49-73 


51.00 


52.28 


53.55 


54.83 


61.20 


iMe 


47.82 


49.14 


50.48 


51.80 


53.14 


54.46 


55.78 


57.11 


63.7s 


iH 


49.73 


51.10 


52.49 


53.87 


55.25 


56.63 


58.02 


59.40 


66.30 


iiMe 


51.64 


53.07 


54. SI 


SS. 94 


57.38 


58.81 


60.24 


61.68 


68.85 


IM 


53.56 


55.04 


56.53 


58.01 


59.50 


60.99 


62.48 


63.97 


71.40 


Il3/i6 


55.46 


57.00 


58.54 


60.09 


61.62 


63.17 


64.70 


66.24 


73.9s 


I7/^ 


57.38 


58.97 


60.56 


62.16 


63.75 


65.35 


66.94 


68.53 


76.50 


liMe 


59.29 


60.94 


62.58 


64.23 


65.88 


67.52 


69.18 


70.83 


79.0s 


2 


61.20 


62.90 


64.60 


66.30 


68.00 


69.70 


71.40 


73.10 


81.60 



Weights of Flat Rolled Steel per Lineal Foot 135 

Weights of Flat Rolled Steel pee Lineal Foot — (Continued) 



Thick- 


II 


iiH 


iii/^ 


II3/4 


12 


121/4 


I2l/^ 


12?^ 


ness in 
inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


inches 


Me 


7.02 


7.17 


7.32 


7.49 


7.65 


7-82 


7.98 


8.13 


H 


9-34 


9. 57 


9.78 


10.00 


10.20 


10.42 


10.63 


10.84 


V16 


11.68 


11.95 


12.22 


12.49 


12.75 


1301 


13.28 


13.5s 


% 


14 03 


14.35 


14.68 


14.99 


15.30 


15-62 


15.94 


16.26 


Vl6 


16.36 


16.74 


17.12 


17.49 


17.85 


18.23 


18.60 


18.97 


H 


18.70 


19.13 


19.55 


19.67 


20.40 


20.82 


21.25 


21.67 


He 


21.02 


21.51 


22.00 


22.48 


22.95 


23.43 


23.90 


24.39 


H 


23.38 


23.91 


24.44 


24-97 


25.50 


26.03 


26.56 


27.09 


iHe 


25.70 


26.30 


26.88 


27.47 


28.05 


28.64 


29.22 


29.80 


% 


28.05 


28,68 


29.33 


29.97 


30.60 


31-25 


31.88 


32.52 


1^16 


30.40 


31.08 


31.76 


32.46 


33.15 


33-83 


34.53 


35.22 


^ 


32.72 


33.47 


34.21 


34.9s 


35.70 


36.44 


37.19 


37.93 


15/16 


35.06 


35.86 


36.66 


37.46 


38.25 


39 05 


39.84 


40.64 


I 


37.40 


38.25 


39- 10 


39.95 


40.80 


41.65 


42.50 


43.35 


iMe 


• 39-74 


40.64 


41.54 


42.45 


43.35 


44-25 


45.16 


46.06 


ii/i 


42.08 


43.04 


44.00 


44.94 


45.90 


46.86 


47.82 


48.77 


iMe 


44.42 


45.42 


46.44 


47.45 


48.45 


49-46 


50.46 


SI. 48 


iH 


46.76 


47.82 


48.88 


49.94 


51 00 


52.06 


■ 53.12 


54.19 


iMe 


49.08 


50.20 


51.32 


52.44 


53-55 


54-67 


55.78 


56.90 


iH 


51.42 


52.59 


53.76 


54.93 


56.10 


57-27 


58.44 


59.60 


1^6 


53.76 


54.99 


56.21 


57.43 


58.65 


59.87 


61.10 


62.32 


I1/2 


56.10 


57.37 


58.65 


59.93 


61.20 


62.48 


63.75 


65.03 


i^ie 


58.42 


59.76 


61.10 


62.43 


63-75 


65.08 


66.40 


67.74 


iH 


60.78 


62.16 


63 -54 


64.92 


66.30 


67.68 


69.06 


70.44 


iiMe 


63.10 


64.55 


65.98 


67.42 


68.85 


70.29 


71.72 


73. IS 


l3/4 


65.45 


66.93 


68.43 


69.92 


71.40 


72.90 


74.38 


75.87 


11^6 


67.80 


69.33 


70.86 


72.41 


73-95 


75.48 


77.03 


78.57 


1% 


70.12 


71.72 


73.31 


74.90 


76.50 


78.09 


79.69 


81.28 


11^6 


72.46 


74.11 


75.76 


77.41 


79-05 


80.70 


82.34 


83.99 


2 


74.80 


76.50 


78.20 


79.90 


81.60 


83.30 


85.00 


86.70 



The weights. for 12-inch width are repeated on each page to facilitate making the 
additions necessary to obtain the weights of plates wider than 12 inches. Thus to 
find the weight of 15H" X%", add the weights to be found in the same line for 3H X^i 
and 12x^^ = 10.41-1-35.70 = 46.11 pounds. 



136 



Materials 



Weights and Areas of Square and Round Bars of Wrought 
Iron and Circumference of Round Bars. 

One cubic foot weighing 480 lbs. 



Thickness 






Area of 


Area of 


Circum- 


or diam- 


Weight of 

n bar 
I foot long 


Weight of 

bar 
I foot long 


D bar 


bar 


ference of 


eter in 
inches 


in square 
inches 


in square 
inches 


bar 
in inches 




Me 


.013 


.010 


.0039 


.0031 


.1963 


H 


.052 


.041 


.0156 


.0123 


.3927 


3/i6 


.117 


.092 


.0352 


.0276 


.5890 


H 


.208 


.164 


.0625 


.0491 


.7854 


Me 


.326 


.256 


.0977 


.0767 


.9817 


% 


.469 


.368 


.1406 


.1104 


1.1781 


Me 


.638 


.501 


.1914 


.1503 


•1.3744 


H 


.833 


.654 


.2500 


.1963 


1.5708 


%6 


1. 055 


.828 


.3164 


.2485 


I. 7671 


% 


1.302 


1.023 


.3906 


.3068 


1.963s 


iHe 


1.576 


1.237 


.4727 


.3712 


2.1598 


% 


1.875 


1.473 


.5625 


.4418 • 


2.3562 


13/i6 


2.201 


1.728 


.6602 


.5185 


2.SS2S 


^ 


2.552 


2.004 


.7656 


.6013 


2.7489 


iMe 


2.930 


2.301 


.8789 


.6903 


2.9452 


I 


3.333 


2.618 


I. 0000 


.7854 


3.1416 


He 


3.763 


2.955 


I. 1289 


.8866 


3.3379 


M 


4.219 


3.313 


I . 2656 


.9940 


3.5343 


?i6 


4.701 


3.692 


I . 4102 


I. 1075 


3.7306 


Vi 


5.208 


4.091 


1-5625 


I . 2272 


3.9270 


Me 


5. 742 


4-510 


1.7227 


1.3530 


4.1233 


% 


6.302 


4-950 


1.8906 


1.4849 


4.3197 


Me 


6.888 


5.410 


2.0664 


1.6230 


4.5160 


>i 


7.500 


5.890 


2.2500 


I. 7671 


4.7124 


Me 


8.138 


6.392 


2.4414 


I -9175 


4.9087 


S/^ 


8.802 


6.913 


2.6406 


2.0739 


5.1051 


iMe 


9.492 


7.455 


2.8477 


2.2365 


5.3014 


% 


10.21 


8.018 


3.0625 


2.4053 


5. 4978 


13/(6 


10-95 


8.601 


3.2852 


2.5802 


5 -6941 


H 


11.72 


9.204 


3-5156 


2.7612 


5.890s 


iMe 


12.51 


9.828 


3-7539 


2.9483 


6.0868 


2 


13.33 


10.47 


4.0000 


3.1416 


6.2832 


He 


14.18 


II. 14 


4-2539 


3.3410 


6. 4795 


H 


15 OS 


11.82 


4.5156 


3.5466 


6.6759 


Me 


15-95 


12.53 


4-7852 


3.7583 


6.8722 


H 


16.88 


13.25 


5-0625 


3.9761 


7.0686 


Me 


17.83 


14.00 


5.3477 


4.2000 


7.2649 


?^ 


18.80 


14-77 


5.6406 


4.4301 


7.4613 


Me 


19.80 


15-55 


5.9414 


4.6664 


7.6576 


H 


20.83 


16.36 


6.2500 


4.9087 


7.8540 


Me 


21.89 


17.19 


6.5664 


5.1572 


8.0S03 


5i 


22.97 


18.04 


6.8906 


S.4119 


8.2467 


iHe 


24.08 


18.91 


7.2227 


5.6727 


8.4430 


% 


25.21 


19.80 


7.562s 


5.9396 


8.6394 


iMe 


26.37 


20.71 


7.9102 


6.2126 


8.8357 


% 


27.55 


21.64 


8.2656 


6.4918 


9-0321 


iMe 


28.76 


22.59 


8.6289 


6.7771 


9.2284 



Weight of Square and Round Bars 



137 



Weight of Square and Round Bars — (Continued) 



Thickness 
or diam- 


. Weight of 
D bar 
I foot long 


Weight of 

bar 
I foot long 


Area of 
a bar 


Area of 
bar 


Circum- 
ference of 


eter in 
inches 


in square 
inches 


in square 
inches 


bar 
in inches 


3 


30.00 


23.56 


9.0000 


7.0686 


9.4248 


Me 


31 26 


24.55 


9.3789 


7.3662 


9.6211 


H 


32.55 


25.57 


9-7656 


7.6699 


9.8175 


3/16 


33.87 


26.60 


10.160 


7.9798 


10.014 


H 


35.21 


27.65 


10.563 


8.2958 


10.210 


^16 


36.58 


28.73 


10.973 


8.6179 


10.407 


H 


37.97 


29.82 


II. 391 


8.9462 


10.603 


Vxo 


39-39 


30.94 


II. 816 


9.2806 


10.799 




40.83 


32.07 


12.250 


9.6211 


10.996 


42.30 


33.23 


12.691 


9-9678 


II. 192 


% 


43.80 


34.40 


13. 141 


10.321 


11.388 


iMe 


45. 33 


35.60 


13.598 


X0.680 


II. 58s 


% 


46.88 


36.82 


14.063 


II.04S 


II. 781 


13/16 


48.45 


38.05 


14-535 


II. 416 


11.977 


^^ 


50.0s 


39-31 


IS.016 


11-793 


12.174 


15/6 


51.68 


40.59 


15.504 


12.177 


12.370 


4 


53.33 


41.89 


16.000 


12.566 


12.566 


Me 


55. 01 


43-21 


16.504 


12.962 


12.763 


1/^ 


56.72 


44.55 


17.016 


13.364 


12.959 


3/6 


58.45 


45.91 


17.535 


13-772 


13.ISS 


M 


60.21 


47.29 


18.063 


14.186 


13 352 


5/6 


61.99 


48.69 


18.598 


14.607 


13.548 


% 


63.80 


50.11 


19. 141 


15.033 


13.744 


VlQ 


65.64 


51.55^ 


19.691 


15.466 


13.941 


Vl 


67.50 


53.01 


20.250 


IS -904 


14.137 


%6 


69.39 


54.50 


20.816 


16.349 


14.334 


^A 


71-30 


56.00 


21.391 


16.800 


14.530 


iMe 


73.24 


57.52 


21.973 


17-257 


14.726 


% 


75.21 


59.07 


22.563 


17.721 


14.923 


1^6 


77.20 


60.63 


23.160 


18.190 


15. 119 


^ 


79.22 


62.22 


23.766 


18.665 


15.31S 


IMe 


81.26 


63.82 


24.379 


19-147 


15.512 


5 


83.33 


65.45 


25.000 


19-635 


15.708 


Me 


85.43 


67.10 


25.629 


20.129 


15.904 


H 


87.55 


68.76 


26.266 


20.629 


16.101 


Me 


89.70 


70.45 


26.910 


21 . 135 


16.297 


M 


91.88 


72.16 


27-563 


21.648 


16.493 


Me 


94.08 


73.89 


28.223 


22.166 


16.690 


% 


96.30 


75.64 


28.891 


22.691 


16.886 


^6 


98.55 


77.40 


29.566 


23.221 


17.082 


H 


100.8 


79.19 


30.250 


23.758 


17.279 


Me 


103. 1 


81.00 


30.941 


24-301 


17-475 


H 


105.5 


82.83 


31.641 


24.850 


17.671 


iMe 


107.8 


84.69 


32.348 


25.406 


17.868 


% 


no. 2 


86.56 


33.063 


25.967 


18.064 


13/6 


112. 6 


88.45 


33.785 


26.535 


18.261 


^ 


115. 1 


90.36 


34.516 


27.109 


18.457 


iMe 


117. S 


92.29 


35.254 


27.688 


18.653 


6 


120.0 


94.25 


36.000 


28.274 


18.8S0 


M« 


122. 5 


96.22 


36.754 


28.866 


19.046 


^ 


125. 1 


98.22 


37.516 


29.465 


19.242 


Me 


127.6 


100.2 


38.28s 


30.069 


19.439 



138 



Materials 



Weight of Square and 


Round Bars — {Continued) 


Thickness 
or diam- 


Weight of 

D bar 
I foot long 


Weight of 

bar 

I foot long 


Area of 
D bar 


Area of 
bar 


Circum- 
ference of 


eter in 
inches 


in square 
inches 


in square 
inches 


bar 
in inches 


m 


130.2 


102.3 


39-063 


30.680 


19.635 


Me 


132.8 


104.3 


39.848 


31.296 


19.831 


?^ 


135.5 


106.4 


40.641 


31-919 


20.028 


Mo 


138. 1 


108.5 


41.441 


32.548 


20.224 


H 


140.8 


no. 6 


42.250 


33.183 


20 . 420 


%6 


143.6 


112. 7 


43.066 


33.824 


20.617 


% 


146.3 


114. 9 


43.891 


34.472 


20.813 


1H6 


149. 1 


117. 1 


44-723 


35-125 


21.009 


% 


151. 9 


II9-3 


45.563 


35-785 


21.206 ^ 
21.402 ^ 


13/(6 


154.7 


121. 5 


46.410 


36.450 


% 


157.6 


123.7 


47.266 


37-122 


21.598 


1^6 


160.4 


126.0 


48.129 


37-800 


21.795 


7 


163.3 


128.3 


49000 


38-485 


21.991 


Me 


166.3 


130.6 


49.879 


39-175 


22.187 


H 


169.2 


132.9 


50.766 


39-871 


22.384 


M« 


172.2 


135.2 


51.660 


40-574 


22.580 


M 


175.2 


137.6 


52.563 


41.282 


22.777 


Ma 


178.2 


140.0 


53.473 


41.997 


22.973 


H 


181. 3 


142.4 


54-391 


42.718 


23.169 


M« 


184.4 


144.8 


55-316 


43.445 


23.366 


H 


187.5 


147.3 


56.250 


44.179 


23.562 


9i6 


190.6 


149-7 


57.191 


44.918 


23.758 


5i 


193.8 


152.2 


58.141 


45 664 


23.955 


iMe 


197.0 


154.7 


59 098 


46.415 


24.151 


% 


200.2 


157.2 


60.063 


47.173 


24.347 


1^6 


203.5 


159-8 


61.035 


47.937 


24.544 


% 


206.7 


162.4 


62.016 


48.707 


24.740 


»M6 


210.0 


164.9 


63.004 


49-483 


24.936 


8 


213.3 


167.6 


64.000 


50.265 


25.133 


Mfl 


216.7 


170.2 


65.004 


51.054 


25.329 


H 


220.1 


172.8 


66.016 


51-849 


25.52s 


Ms 


223.5 


175.5 


67-035 


52.649 


25.722 


M 


226.9 


178.2 


68.063 


53.456 


25-918 


Ms 


230.3 


180.9 


69.098 


54.269 


26.114 


?i 


233.8 


183.6 


70.141 


55-088 


26.311 


Me 


237.3 


186.4 


71. 191 


55-914 


26.507 


H 


240.8 


189.2 


72.250 


56.745 


26.704 


Me 


244.4 


191-9 


73.316 


57.583 


26.900 


% 


248.0 


194-8 


74.391 


58.426 


27.096 


iHe 


251.6 


197-6 


75.473 


59.276 


27.293 


% 


255.2 


200.4 


76.563 


60.132 


27-489 


iMo 


258.9 


203.3 


77-660 


60.994 


27.685 


^ 


262.6 


206.2 


78.766 


61.862 


27.882 


»M6 


266.3 


209.1 


79.879 


62.737 


28.078 


9 


270.0 


212. 1 


81.000 


63.617 


28.274 


Me 


273.8 


215.0 


82.129 


64.504 


28.471 


H 


277.6 


218.0 


83.266 


65.397 


28.667 


Me 


281.4 


221.0 


84.410 


66.296 


28.863 


M 


285.2 


224.0 


85.563 


67.201 


29.060 


Me 


289 I 


227.0 


86.723 


68.112 


29.256 


?^ 


293.0 


230.1 


87.891 


69.029 


29.452 


Me 


296.9 


233.2 


89.066 


69.953 


29.649 



Weight of Square and Round Bars 



130 



Weight of Square and Round Bars — {Continued) 



Thickness 
or diam- 


Weight of 
D bar 


Weight of 
bar 


Area of 
D bar 


Area of 
bar 


Circum- 
ference of 


eter in 
inches 


I foot long 


I foot long 


in square 
inches 


in square 
inches 


bar 
in inches 


m 


300.8 


236.3 


90.250 


70.882 


29.845 


ri6 


304.8 


239.4 


91.441 


71.818 


30.041 


% 


308.8 


242.5 


92.641 


72.760 


36.238 


iMe 


312.8 


245.7 


93.848 


73.708 


30.434 


% 


316.9 


248.9 


95.063 


74.662 


30.631 


1^6 


321.0 


252.1 


96.285 


75.622 


30.827 


% 


325.1 


255.3 


97.516 


76.589 


31.023 


1^6 


329.2 


258.5 


98.754 


77.561 


31.200 


lO 


333.3 


261.8 


100.00 


78.540 


31.416 


H8 


337.5 


265.1 


101.25 


79.525 


31.612 


H 


341.7 


268.4 


102 . 52 


80.516 


31.809 


^6 


346.0 


271.7 


103.79 


81.513 


32.005 


H 


3S0.2 


275.1 


105.06 


82.516 


32.201 


Me 


354.5 


278.4 


106.35 


83.525 


32.398 


% 


358.8 


281.8 


107.64 


84.541 


32.594 


^8 


363.1 


285.2 


108.94 


85.562 


32.790 


H 


367.5 


288.6 


110.25 


86.590 


32.987 


916 


371.9 


292.1 


III. 57 


87.624 


33.183 


% 


376.3 


295.5 


112.89 


88.664 


33.379 


»M6 


380.7 


299.0 


114.22 


89.710 


33.576 


% 


385.2 


302.5 


115.56 


90.763 


33.772 


1^6 


389.7 


306.1 ^ 


116. 91 


91.821 


33.968 


% 


394.2 


309.6 


118.27 


92.886 


34.165 


1^6 


398.8 


313.2 


119.63 


93.956 


34.361 


II 


403.3 


316.8 


121.00 


95.033 


34.558 


He 


407.9 


320.4 


122.38 


96.116 


34.754 


H 


412.6 


324.0 


123.77 


97.205 


34.950 


5i6 


417.2 


327.7 


125.16 


98.301 ■ 


35.147 


H 


^21.9 


331.3 


126.56 


99.402 


35.343 


Me 


426.6 


335.0 


127.97 


100. .51 


35.539 


% 


431.3 


338.7 


129.39 


101.62 


35.736 


^6 


436.1 


342.5 


130.82 


102.74 


35.932 


^ 


440.8 


346.2 


132.25 


103.87 


36.128 


Ma 


445.6 


350.0 


133.69 


105.00 


36.32s 


5i 


4S0.5 


353.8 


135.14 


106.14 


36.521 


»Me 


455.3 


357.6 


136.60 


107.28 


36.717 


% 


460.2 


361.4 


138.06 


108.43 


36.914 


iMe 


465.1 


365.3 


139.54 


109.59 


37.110 


?i 


470.1 


369.2 


141.02 


110.75 


37.306 


iMe 


475.0 


373.1 


142. so 


III. 92 


37.503 



140 Materials 

Weights and Areas of Cold Rolled Steel Shafting 



Diam- • 


Area, 


Circum- 


Weight 


Diam- 


Area, 


Circum- 


Weight 


eter, 


square 


ference, 


per foot, 


eter, 


square 


ference, 


per foot. 


inches 


inches 


inches 


pounds 


inches 


inches 


inches 


pounds 


He 


.0276 


.5890 


.095 


23/6 


3.7583 


6.8722 


12.80 


H . 


.0491 


:7854 


.167 


2yi 


3.9761 


7.0686 


13.52 


Vie 


.0767 


.9817 


.260 


25/6 


4.2000 


7.2749 


14.35 


H 


.1104 


1.1781 


.375 


2H 


4.4301 


7.4613 


15.07 


^6 


.1503 


1.3744 


.511 


2^6 


4.6664 


7.6576 


IS. 89 


H 


.1963 


1.5708 


.667 


21/ 


4.9087 


7.8540 


16.70 


9i6 


.2485 


I. 7671 


.845 


2916 


5.1572 


8.0503 


17.55 


H 


.3068 


1.9635 


1.05 


25i 


5.4119 


8.2467 


18.41 


^Me 


.3712 


2.1598 


1.26 


211/6 


5.6727 


8.4430 


19.31 


H 


.4418 


2.3562 


1.50 


2% 


5.9396 


8.6394 


20.21 


1^6 


.5185 


2.5525 


1.77 


21 %6 


6.2126 


8.8357 


21.15 


% 


.6013 


2.7489 


2.05 


2% 


6.4918 


9.0321 


22.09 


1^6 


.6903 


2.9452 


2.35 


215/6 


6.7771 


9.2284 


23.06 


I 


.7854 


3.1416 


2.68 


3 


7.0686 


9.4248 


24.05 


iHe 


.8866 


3.3379 


3.02 


31/ 


7.6699 


9.8175 


26.09 


iH 


.9940 


3.5343 


3.38 


33/6 


7.9798 


10.014 


27.16 


I3/16 


I . 1075 


3.7306 


3.77 


3/4 


8.2958 


10.210 


28.22 


m 


1.2272 


3.9270 


4.17 


33/ 


8.9462 


10.603 


30.43 


iMe 


I.3S30 


4.1233 


4.61 


3M6 


9.2806 


10.799 


31.58 


1% 


1.4849 


4.3197 


5.05 


31/ 


9.6211 


10.996 


32.73 


17/16 


1.6230 


4.5160 


5.52 


3% 


10.321 


11.388 


35.20 


iH 


I. 7671 


4.7124 


6.01 


311/6 


10.680 


11.585 


36.40 


I9i6 


I. 9175 


4.9087 


6.52 


33/i 


II. 04s 


11.781 


37.57 


I5i 


2.0739 


5.1051 


7.06 


3H 


11.793 


12.174 


39.40 


iiHe 


2.2365 


5.3014 


7.61 


315/6 


12.177 


12.370 


41.04 


134 


2.4053 


5.4978 


8.18 


4 


12.566 


12.566 


42.75 


113/16 


2.5802 


5.6941 


8.78 


4K 


14.186 


13.352 


48.26 


m 


2.7612 


5.8905 


9.39 


4^6 


IS. 466 


13.941 


52.62 


11^6 


2.9483 


6.0868 


10.03 


41/ 


15.904 


14.137 


54.11 


2 


3.1416 


6.2832 


10.69 


43/ 


17.728 


14.923 


60.88 


2H6 


3.3410 


6.479s 


11.35 


41 Me 


19.147 


15.512 


65.50 


2>i 


3.5466 


6.6759 


12.07 


5 


19.635 


15.708 


67.4s 



Corrugated Iron Roofing 



141 



Sheet Iron 

Weight of a superficial foot. 



Number of 


Weight per 


Number of 


Weight per 


gauge 


foot 


gauge 


foot 


I 


11.25 


l6 = M6 


2.5 


2 


10.625 


17 


2.1875 


3=Vi 


10.00 


18 


1.875 


4 


9-375 


19 


I. 7188 


5 


8.750 


20 


1.562s 


6 


8.125 


21 


1.4063 


7 


7.50 


22=1.^2 


I . 2500 


8 


6.875 


23 


1. 120 


9 


6.250 


24 


1. 000 


10 


5.625 


25 


.900 


II =H 


5000 


26 


.800 


12 


4.375 


27 


.720 


13 


3.750 


28 


.640 


14 


3.125 


29 


.560 


15 


2.8125 


30 


.500 



Galvanized Sheet Iron 

Am. Galv. Iron Ass'n. B. W. G. 



No. 


Ounces 
avoir. 

per 

square 

foot 


Square 
feet per 

2240 
pounds 


No. 


Ounces 
avoir. 

per 

square 

foot 


Square 
feet per 

2240 
pounds 


No. 


Ounces 
avoir. 

per 

square 

foot 


Square 
feet per 
. 2240 
pounds 


29 
28 
27 
26 
25 


12 
13 
14 
IS 
16 


2987 
2757 
2560 
2389 
2240 


24 
23 
22 

21 . 
20 


17 
19 
21 
24 
28 


2108 
1886 
1706 
1493 
1280 


19 
18 
17 
16 
14 


33 
38 
43 
48 
60 


1084 
943 
833 
746 
597 



Corrugated Iron Roofing 



B. W. 
gauge 


Weight per square 

(100 square feet). 

Plain 


Galvanized 


Number 
28 
26 
24 
22 
20 
18 
16 


Pounds 
97 
los 
128 
150 
18S 
270 
340 


Weighs from 5 to 15 per cent 
heavier than plain, accord- 
ing to the number B. W. G. 



Allow one-third the net width for lapping and for corrugations. 
2}i to 3}^ pounds for rivets will be required per square. 



From 



142 



Materials 
Sizes and Weight of Sheet Tin 





Number of 

sheets in 

box 


Dimension 


Weight of 


Mark 


Length, 
inches 


Breadth, 
inches 


box, 
pounds 


iC 


225 
225 
225 
225 
225 
225 
225 

lob 

ICO 
ICO 
IOC 
lOO 
200 
20O 
200 
200 
225 


13H 

13)4 

12% 

13% 

13% 

13% 

13% 

i6% 

i6% 

i6% 

i6% 

l6% 

15 

15 

15 

15 

13% 


lo 
9% 

lO 

lO 

lO 

lO 

I2l/^ 

12^ 

I2l^ 

I2l^ 

I2l^ 

II 

II 

II 

II 

lO 


112 


iiC 


loS 


iiiC 


98 


iX 


140 


iXX 


161 


iXXX 


182 


iXXXX 


203 


DC 


los 


DX 


126 


DXX 


147 


DXXX 


168 


DXXXX 


189 


SDC 


168 


5DX 


189 


SDXX 


21Q 


SDXXX 


231 


iCW . 


112 







A box containing 225 sheets, 13% by 10, contains 214.84 square feet; 
but allowing for seams it will cover only 150 square feet of roof. 
A roof covered with metal should slope not less than i inch to the foot. 



Weights of Sheet Metals per Square Foot 



Thick- 


Wrought 


Cast 


Steel, 


Copper. 


Brass, 


Lead, 


Zinc, 


inches 


pounds 


pounds 


pounds 


pounds 


pounds 


pounds 


pounds 


Me 


2.53 


2.34 


2.55 


2.89 


2.73 


3.71 


2.34 


H 


5.05 


4.69 


5.10 


5.78 


5.47 


7.42 


4.69 


%6 


7.58 


7.03 


7.66 


8.67 


. 8.20 


II. 13 


7.03 


H 


10.10 


9.38 


10.21 


11.56 


10.94 


14.83 


9.38 


Me 


12.63 


11.72 


12.76 


14.45 


13.67 


18.54 


11.72 


H 


15 16 


14.06 


15.31 


17.34 


16.41 


22.25 


14.06 


Me 


17.68 


16.41 


17.87 


20.23 


19.14 


25.96 


16.41 


^ 


20.21 


18.75 


20.42 


23.13 


21.88 


29.67 


18.7s 


H 


25.27 


23.44 


25.52 


28.91 


27.34 


37.08 


23-44 


% 


30.31 


28.13 


30.63 


34.69 


32.81 


44.50 


28.13 


-"A 


35-37 


32.81 


35.73 


40.47 


38.28 


51.92 


32.81 


I 


40.42 


37.50 


40.83 


46.2s 


43.75 


59-33 


37-50 



Weight of Copper and Brass Wire and Plates 



143 



Weight or Copper and Brass Wire and Plates 

Brown and Sharpe Gauge. 







Weight of wire per 


Weight of plates per 


No. of 


Size of 


1000 lineal feet 


square foot 




each no.. 










gauge 












inch 


Copper, 


Brass, 


Copper, 


Brass, 






pounds 


pounds 


pounds 


pounds 


0000 


.46000 


640.5 


605-28 


20.84 


19.69 


000 


.40964 


508.0 


479-91 


18.55 


17.53 


00 


.36480 


402.0 


380.77 


16.52 


15.61 





.32476 


319-5 


301.82 


14-72 


13.90 


I 


.28930 


253-3 


239-45 


13.10 


12.38 


2 


.25763 


200.9 


189.82 


11.67 


11.03 


3 


.22942 


159-3 


150.52 


10.39 


9.82 


4 


.20431 


126.4 


119.48 


9.25 


8.74 


5 


.18194 


100.2 


94-67 


8.24 


7.79 


6 


. 16202 


79-46 


75.08 


7.34 


6.93 


7 


.14428 


63.01 


59. 55 


6.54 


6.18 


8 


.12849 


49.98 


47.22 


5.82 


5.50 


9 


.11443 


39-64 


37.44 


5.18 ^ 


4-90 


10 


.10189 


31-43 


29-69 


4-62 


4-36 


II 


.090742 


24.92 


23.55 


4. II 


3-88 


12 


.080808 


19-77 


18.68 


3-66 


3-46 


13 


.071961 


15-65 


14.81 


3-26 


3.08 


14 


.064084 


12.44 


11.75 


2.90 


2.74 


15 


.057068 


9.86 


9.32 


2.59 


2.44 


16 


.050820 


7.82 


7.59 


2.30 


2.18 


17 


.045257 


6.20 


5.86 


2.05 


1.94 


18 


.040303 


4.92 


4.65 


1.83 


1.72 


19 


.035890 


390 


3.68 


1.63 


1.54 


20 


.031961 


3.09 


2.92 


1-45 


1.37 


21 


.028462 


2.45 


2.317 


1.29 


1.22 


22 


.025347 


1.94 


1.838 


1. 15 


1.08 


23 


.022571 


1.54 


1.457 


1.02 


.966 


24 


.020100 


1.22 


1. 155 


-911 


.860 


25 


.017900 


.699 


.916 


.811 


.766 


26 


.01494 


.769 


.727 


.722 


.682 


27 


.014195 


.610 


.576 


.643 


.608 


28 


.012641 


.484 


.457 


.573 


.541 


29 


.011257 


.383 


.362 


.510 


.482 


30 


.010025 


.304 


.287 


.454 


.429 


31 


.008928 


.241 


.228 


.404 


.382 


32 


.007950 


.191 


.181 


.360 


.340 


33 


.007080 


.152 


.143 


.321 


.303 


34 


.006304 


.120 


.114 


.286 


.270 


35 


.005614 


.096 


.0915 


.254 


.240 


36 


.005000 


.0757 


.0715 


.226 


.214 


37 


.004453 


.0600 


.0567 


.202 


.191 


38 


.003965 


.0467 


.0450 


.180 


170 


39 


.003531 


.0375 


.0357 


.160 


iSi ' 


40 


.003144 


.0299 


.0283 


.142 


.135 


Specific gravit 


y 


8.880 


8.386 


8.698 


8.218 


Weight per cu 


oicfoot 


555 


524.16 


543.6 


513.6 



144 



Materials 
Weight of Sheet and Bar Brass 





Sheets 


Square 


Round 




Sheets 


Square 


Round 


Thick- 


per 


bars 


bars 


Thick- 


per 


bars 


bars 


ness, 


square 


I foot 


I foot 


ness, 


square 


I foot 


I foot 


inches 


foot, 


long, 


long, 


inches 


foot. 


long, 


long, 




pounds 


pounds 


pounds 




pounds 


pounds 


pounds 


Me 


2.7 


.015 


.011 


iHe 


45.95 


4.08 


3.20 


H 


5.41 


.055 


.045 


iH 


48.69 


4.55 


3 


57 


3/16 


8.12 


.125 


.1 


I^/ls 


51.4 


5.08 


3 


97 


H 


10.76 


.225 


.175 


iM 


54.18 


5.65 


4 


41 


Ms 


13.48 


.350 


.275 


1M6 


65.85 


6.22 


4 


86 


H 


16.25 


.51 


.395 


1% 


59.55 


6.81 


5 


35 


ViO 


19 


.69 


.54 


iMe 


62.25 


7.45 


5 


85 


Vi 


21.65 


.90s 


.71 


1K2 


65 


8.13 


6 


37 


9i6 


24.3 


1. 15 


■ 9 


l9/i6 


67.75 


8.83 


6 


92 


5/i 


27.13 


1.4 


I.I 


\% 


70.35 


9-55 


7 


48 


^He 


29.77 


1.72 


1.35 


iiMe 


73 


10.27 


8 


05 


% 


32.46 


2.05 


1.66 


1% 


75.86 


II 


8 


65 


iS/'ie 


35.18 


2.4 


1.85 


iiMe 


78.55 


11.82 


9 


29 


?i 


37.85 


2.75 


2.15 


-I'A 


81.25 


12.68 


9 


95 


iMe 


40.55 


3.15 


2.48 


iiMe 


84 


13. 5 


10 


58 


I 


43.29 


3.65 


2.85 


2 


86.75 


14.35 


II 


25 



Weight of Round Bolt Copper per Foot 



Diameter, 
inches 


Pounds 


Diameter, 
inches 


Pounds 


Diameter, 
inches 


Pounds 


% 


.425 

.756 

1. 18 

1.70 

2.31 


I 
1% 


3.02 
3.83 
4.72 
5-72 
6.81 


m 

Hi 

2 


7.99 
9.27 
10.64 
12.10 









Areas and Weights of Fillets of Steel, Cast Iron and Brass 145 



Areas and Weights of Fillets of Steel, Cast Iron 
AND Brass 

Calculations are based on the following weights: 

Steel 489 . 6 pounds per cubic foot. 

Cast iron 45° 

Cast brass S04 




Fig. 39. 




Contributed by Ernest J. Lees. 



146 



Materials 



Gauges and Weights of Iron Wire 

The sizes and weights from No. 20 to No. 40 are those of the Trenton Iron Co. 
Trenton, N. J. 



No. 


Diameter, 


Lineal feet 


No. 


Diameter, 


Lineal feet 


inches 


to the pound 


inches 


to the pound 


21 


.031 


392.772 


31 


.013 


2232.653 


22 


.028 


481.234 


32 


.012 


2620.607 


23 


.025 


603.863 


33 


.011 


31 19 092 


24 


.0225 


745.710 


34 


.010 


3773.584 


25 


.020 


943.396 


35 


.0095 


4182.508 


26 


.018 


1164.689 


36 


.009 


4657.728 


27 


.017 


1305.670 


37 


.0085 


5222.035 


28 


.016 


1476.869 


38 


.008 


5896.147 


29 


•ois 


1676.989 


39 


.0075 


6724.291 


30 


.014 


1925.321 


40 


.007 


7698.253 



American Steel & Wire Company 



Full sizes of plain wire 




Fig. 40. 



Gauge 



Diameter 
of Amer- 
ican Steel 

«&Wire 
Co. 's gauge 



.2830 
.2625 
.2437 

.2253 

.2070 
.1920 
.1770 
.1620 
.1483 
.1350 
.1205 
.1055 
.0915 
.0800 
.0720 
.0625 
.0540 
.0475 
.0410 
.0348 



Weight 

one mile, 

pounds 



1128.0 
970.4 
836.4 
714.8 
603.4 
519.2 
441.2 
369.6 
309 -7 
256.7 
204.5 
156.7 
117. 9 
90.13 
73.01 
55.01 
41.07 
31.77 
23.67 
17.05 



Feet to 
pound 



4.681 
5.441 
6.313 
7.386 
8.750 



11.97 

14.29 

17.05 
20.57 
25.82 
33.69 
44.78 
58.58 
72.32 
95.98 
128.6 
166.2 
223.0 
309.6 



Iron Wire 



147 



Iron Wire 

Measured by Washburn & Moen gauge. List prices per pound. 



No. 


-Bright Galv^j 
market wire "'^f^ 


lized 
iet 


Annealed 
stone wire, 
bright or 


Tinned 
market 


Tinned 
stone 








black 


wire 


wire 


ooooto9 


$0.10 $0 


10 




$o.is 




lo and II 


.11 


II 




.16 




12 


• iii/i 


11I/2 




.17 




13 and 14 


.12}-^ 


12H 




.17 




15 


.14 


14 




.I7i/i 




16 


.14 


14 


$0.14 


.17}-^ 




17 . 


IS 


15 


.15 


.18 




18 


.16 


16 


.16 


.18^ 


$o.i8H 


19 


• 19 


19 


• 19 




.19 
.19 
.20 


20 


.20 
.21 
.22 
.23 


20 
21 
22 
23 


.20 

.21 

.22 

/ .23 




21 




22 




.20 


23 




.21 


24 


■ 24 


24 


.24 




21 


25 


.25 


25 


.25 




.22 


26 


.26 

.28 


26 
28 


.26 
.28 




.23 


27 




.24 


28 


.29 


29 


.29 
.30 






29 


•30 


30 




.26 


30 


• 32 


32 


,32 




.27 


31 


.33 


33 


.33 




.28 


32 


• 35 


35 


.35 




.32 


33 


.37 


37 


.37 




.33 


' 34 


.40 


40 


.40 




.34 


35 


• 45 


45 


.45 




36 


.55 


55 


.55 




.48 









• Coppered Market Wire and Coppered Bessemer Spring Wire take same list prices 
Bright Market Wire. 



148 



Materials 



Nails and Tacks 

Common Wire Nails 
Measured by Washburn & Moen Gauge 





Length and gauge 


Approx. 


Size 




no. to 








Inch 


No. 


pound 


■ 2d 


I 


IS 


876 


3d 


iH 


14 


568 


4d 


iH 


12^ 


316 


5d 


l3/i 


I2l/^ 


271 


6d 


2 


Il^i 


181 


7d 


2l/i 


II3/2 


161 


8d 


2\<l 


ioi/4 


106 


9d 


2% 


ioi/4 


96 


lod 


3 


9 


69 


I2d 


3^/4 


9 


63 


i6d 


3^2 


8 


49 


20d 


4 


6 


31 


3od 


4K2 


5 


24 


4od 


5 


4 


18 


5od 


51/2 


3 


14 


6od 


6 


2 


II 



Length and Number of Tacks to the Pound 



Name, 


Length, 


No. to the 


Name, 


Length, 


No. to the 


ounces 


inches 


pound 


ounces 


inches 


pound 


I 


% 


16,000 


10 


iMs 


1600 


m 


3/i6 


10,666 


12 


% 


1333 


2 


H 


8,000 


14 


1^6 


1143 


2M 


Me 


6,400 


16 


% 


1000 


3 


% 


5,333 


18. 


me 


888 


4 


7/i6 


40,000 


20 


I 


800 


6 


9/6 


2,666 


22 


iHe 


727 


8 


5/i 


2,000 


24 


i\i 


666 



United States Standard Threads 
United States Standard Threads 



149 











Size of tap 




Safe load 






Diametet of 


drill, giving a 
clearance of 




on threaded 
bolt on 


Nominal 


No. of 


tap at root of 


i/i the height of 


Area at 


basis of 


diarneter of 


threads 


thread 


the original 


root of 


6000 pounds 


screw, 


per 






thread triangle 


thread. 


stress per 


inches 


inch 








square 
inches 


sq. in. of 
section at 
















root of 


' 




Inches 


Nearest 
64ths 


Inches 


Nearest 
64ths 




. thread, 
pounds 


H 


.250 


20 


.185 


3/i6 - 


.196 


13/64- 


.027 


162 


Me 


.312 


18 


.240 


15/64 + 


.252 


H + 


.045 


270 


% 


.375 


16 


.294 


1%4- 


.307 


5/6 - 


.068 


408 


^6 


.437 


14 


.345 


11/^2 + 


.360 


23/64 + 


.093 


558 


H 


.500 


13 


.400 


13/32- 


.417 


2/64- 


.126 


756 


Me 


.562 


12 


.454 


2%4 + 


.472 


15/^2 + 


.162 


997 


^A 


.62s 


II 


.507 


y2 "+ 


.527 


1%2- 


.202 


1,210 


iHe 


.687 


II 


.569 


ri6 + 


.589 


19^2- 


.254 


1,520 


% 


.750 


10 


.620 


5/8 - 


.642 


*l/64 + 


.302 


1,810 


1^6 


.812 


10 


.683 


11/16- 


.704 


4%4 + 


.366 


2,190 


% 


.875 


9 


.731 


4^64- 


.755 


3/4 + 


.420 


2,520 


iMe 


.937 


9 


.793 


51/64- 


.817 


13/16 + 


.494 


2,960 


I 


1. 000 


8 


.838 


27/^2- 


.865 


55/64 + 


.551 


3,300 


iHe 


1.062 


8 


.900 


2%2- 


.927 


59/64 + 


.636 


3,810 


iH 


1. 125 


7 


.939 


15/6 + 


.970 


31/32 + 


.694 


4,160 


iMe 


1. 187 


7 


1.002 


I + 


1.032 


1H2 + 


.788 


4,720 


iH 


1.250 


7 


1.064 


IM5 + 


1.095 


13/32 + 


.893 


5,3So 


iH 


1.375 


6 


1. 158 


15/32 + 


1. 215 


I%2 - 


1.057 


6,340 


i^ 


1.500 


6 


1.283 


19/32 + 


1.345 


111/^2 + 


1.295 


7.770 


iH 


1.625 


51/2 


1.389 


125/64- 


1.428 


12/64 + 


1. 515 


9.090 


m 


I.7SO 


5 


1.490 


131/64 + 


1.534 


117/^2 + 


1.746 


10,470 


m 


1.875 


5 


1. 615 


13 9/64 + 


1.659 


121/32 + 


2.051 


12,300 


2 


2.000 


4^2 


1. 711 


12^32- 


1.760 


14^64 - 


2.302 


13,800 


2H 


2.250 


4K2 


1. 961 


161/64 + 


2.010 


2I.64 - 


3.023 


18,100 


2K 


2.500 


4 


2.175 


211/64 + 


2.230 


215/64- 


3.719 


22,300 


2% 


2.750 


4 


2.425 


22/64 + 


2.480 


231/64- 


4.620 


27,700 


3 


3.000 


3^2 


2.629 


25/8 + 


2.691 


211/6 + 


5.428 


32,500 


3H 


3.250 


3^2 


2.879 


2% + 


2.941 


215/6 + 


6.510 


39,000 


SVi 


3.500 


3H 


3- 100 


33/32 + 


3.167 


31^64- 


7.548 


45,300 


3% 


3.750 


3 


3.317 


35/6 + 


3.389 


325/64- 


8.641 


51,800 


4 


4.000 


3 


3.567 


39/16 + 


3.639 


3*1/64- 


9.963 


59.700 



150 



Materials 



to 

M 


1 


•ui -bs 
J9d -sqi 
OOO'OI :^v 


M M ei fO ^ .o<0 « O t. JO t^ O r^ g t^jO 


•m -bs 
jad -sqi 
oo£A :^v 




1 

3 
fo 


•ui -bs 

jad -sqi 

ooo'oi '^v 


MMM^,ro^Ot^a.^^^^O^^^M^O;0^ 


•UT •bs 
jad -sqi 
ooSi W 


H M M of ro -* .O t^ C^ M ro tooo O JO a>0 5 


1 


•UT -bs jad 


'^t-MO <N0O lOM rOO M lD-*<0 lOU^OO (NOO OOO 

M M ^^ N ro -? t: <^ of JO 00 gj O O JO g N ^^- 


•UT -bs jsd 
•sqi ooS'zi ^V 




■ut -bs jad 
•sqt ooo'oi q.v 


M H (N ro '^f lO <0 oo" O N JO t^ O ro g^ t;^ <0 


i 


JO uionog 


Oi^oOrOI>wooorOOw0^i-iooa>MQMfOrO<0 
(O lor-roiON M <N O^H rOa>TfrO'*^*0 mO 0> 

OOOOi-<MCsr0^iO<0000<N'iOt^OroOt~>0 


HHHHNNfOfO-^ 


^pa 




HWMNtNNfOro-^tO 






CTioO^OiO^i^O OOiorO OOioro OOtO >0 

MHHMHMHIHt-lN 




VO lO lO 

(N10I> Olio lO lO >0 lO »0 
lOwt^fJ lOtN10I> CS10t> tSlOt^ »0 lO 
<NOOrO'*iOiO<Ot--00 M(NroiOOt--00 C^lOl> 

M W C-i H H l-i H H N n' Cq «' 


Q 


p^ajq^ 
JO mo^^^og; 


05oo^M^a>M^o^5^;ooog«,r<,rjc.N 

OO^oi^S lOO 0^ r5^rorO<OIooooO CT.mm<o I>0< 
M (N <N rO-*^iO<OI>OOOiO w !N ro^Ot^OiM'^r 

W H H M M M H W ei pi 




gls^Sa^sgl^HlstSSISi 


HHMHMMCsiNiNrorOrorO'*-*-* »o »0 




MHMMHHoiiNiNiNoiroi^ro-^'i-'t 




OOlOfOOOlO lO lO lO lO lO 


HMMHiHN(S<N<NiN(NrororC'^ 


1 


qout 
jad spBajqx 


lO lO lO 

ooo^O'*rc<Nw oa>oot-t^<ovoioioiO'*-<t'*-* 


jaq 


aUIBTQ 


OllOt^ (NIO lO lO lO lO lO 

H hI M M H M M M (N N N W 



United States Standard Bolts and Nuts 



iSi 



t^<5^a»M<N o o o>o'*t^N 



a> M (N TT uo i> a> 



es 



00 ooo c5>t^i--'^'^-*a>o^»'JO 
OMi-iQ'^r~"^>^'*oo<OM 
f; 00^ « 00 q> q> "2 o ^1 oo ic "* n 
O 00* vo" ■* "* -^ "1 <o 00 w" ■^ oi r^ 



001HJ>'^fO<^>OOlOt^<NfO 
00 a»M <N ■*ir)t^O%i-i rOtOOO 



ioa»oo looo i>(N •^r'jvo t--* 

Mwiopo-^a^oo 6 '■o m oo in 

P. "^^ "i. °°. ^. "^ 'I H! '^. "^ '^. "v 

f<5 N (N n" -^ O cS pT t^ pT 00 -^ 

lOO t^oo a>o M ro-^vo t^Oi 



00MONl^l^iOlOQ<O0000lO 

oiOiiHNoqNqjoo&io-w Q."-! 

^f<5<NM'<JoCcioOlOt^I>N'^ 

(£5 lO'^lOMOO'OO ■^woo uo^r 
•«tvO<0 H H (N i/^iot^oo rrt^oo 

iC m" T? oo~ tJ m" cfi t^ i> a> o" »o 00 
^ooo a>o N -^tot^cyvM ■<^»ooo 

t;-(N M cqcftMuiiDo^inoo Ot^ 

rfuiioo cfir<5t>pft-tioPrNO 
lOvD t^OO OiM (N 'tiot^Oiw t^ 

MMtHMMMPJN 

l>eiwNO>P«i/5i0O»V500 0t^ 
r^Oi<y.i-ifs O O Oir>'*J><N'* 
W O •^•^iJirO'^M'O t-io lOCTi 

Ttioio<o a>ror~N t^iiioi <m o 

iJi\0- 1> o6 Cr»i-i IN Tt-ioi>-Cr>i-i ro 

OOO M t~Ti-ro<^ir)Oi^fON fO 
qoiCMrfOvO-^OiOt^OOt-'* 
^OOICS '*<O00 O IN rO'*>oy3l> 

o <Nvo o lOH a>t-.io'o t~o»(N 
i>oda>w N «^i/^t-lcrii-I rr> in 00 

MMMMMWC^NOIN 

xf> in m m m m m 

N t^VO<N l>lON t^WPJ 

M oot~-»oio(r)<NM oot^"0 

fOli^>0000<M'<t>000 MfOlO 

N IN ei(N rororOfCPO''*'*-'*--^ 



INlflt^ (NlOt^ NlOt^ 

rr>n^n'^-rf-rt-'rtinininin\o 



§8 


§8 












„ 


^ 




^ 


^ 




H 




-s- 


^ 


J:r 


f^ 


rn 


H, 


in 


8 


SI 




CO 










o 




■^ 


» 


O^ 


•* 


N 


M 


ro 


fC 


r^ 


PO 


■* 


"* 


'^ 


^ 


•<t 


m 


m 


n 


O 


1 


„ 


M 


M 
































^ 




8. 




O 














ro 


rr, 


<£> 


t^ 


J> 


00 


OO 


0-. 


o^ 


o 


O 


M 


^ 


w 


M 


s 


in 


N 


l_l 


'Jl- 


m 


^ 


^ 


r^ 


O 


ro 


2 


Oi 


f: 


J^^'o 


6^ 


s 


?^ 


& 


^ 


^ 


^ 


to 


io<o 


VO 


1^ 


t^ 


«>00 


00 


a> 


O^ 


O 
































•"i-lOUlUHo'vOO t^t>OOodoo' GTi 



in in f^ I 

rO ro t>6 PO f<5 



t^ "O lO »A) ro ro IN 
ei cq <N pi IN cs oi 



fjrorOP^'^-^'t'^iOio 




152 



Materials 



Nuts and Washers, Number to the Pound 

United States Standard Nuts 

Approximate Number in One Hundred Pounds 





Hot pressed 


Cold punched 


Size of 
bolt, 
inches 


Blank 


Tapped 


Plain 


Chamfered, 

trimmed and 

reamed 




Square 


Hexagon 


Square 


Hexagon 


Square 
blank 


Hexa- 
gon 
blank 


Square 
blank 


Hexa- 
gon 
blank 


Mo 
% 

% 

I 

l3/4 

1% 

2 

2H 
2^ 
23^ 
2l^ 
2% 

3 


7200 

40I0 

2540 

1750 

II7S 

910 

6SS 

387 

260 

172 

133 

98 

73 

58 

44 

38 

31 

25 

20 

18 

15 

12 

9 
7 


8400 

5300 

3070 

2080 

1430 

1030 

798 

479 

315 

216 

155 

114 

91 

73 

57 

41 

39 

32 

25 

21 

20 

16 

II 

8H 


7500 
4500 
2720 
1900 
1250 

980 

700 

408 

264 

176 

139 

lOI 

77 

61 

49 

40 

33 

27 

21 

181/^ 

15% 

I2l/i 

9H 
7% 


9000 

5500 

3200 

2170 

1512 

I ISO 

850 

528 

332 

230 

180 

129 

96 

77 

60 

44 

40 

33 

26 

22 

20H 

1X3/4 

9 


6700 
4100 
2400 
1550 

IIOO 

825 

580 

348 

228 

156 

122 

88 

65 

54 

42 

33 

27 

23 

19 

17 


7500 

4700 

2800 

1830 

1300 

990 

700 

438 

290 

198 

140 

103 

77 

63 

50 

39 

31 

28 

24 

20 


7400 

4000 

2730 

1700 

1160 

900 

653 

386 

260 

170 

122 

90 

69 

54 

43 

35 

29 

24 

2oV4 

17 

IS 
12 


8880 

4800 

3276 

2040 

1392 

1080 

784 

463 

312 

204 

146 

108 

83 

65 

52 

42 

35 

29 

26 

23 

20 

16 



Wrought Steel Plate Washers 
Wrought Steel Plate Washers 



153 



Fig. 41. 
In 200-pound Kegs. List prices per 100 pounds. 



Size of 
bolt, 
inches 


Outside 

diameter, 

inches 


Size of hole, 
inches 


Thickness, 

English 

standard 

wire gauge 


Approximate 
number in 
100 pounds 


Per 100 

pounds 








No. 


„ 




Me 


Me 


H 


18 


44.07S 


$14.00 


Vx 


M 


Mfl 


16 


13,84s 


12.20 


Me 


% 


^ 


16 


11,220 


11.40 


% 


I 


Me ^ 


14 


6,573 


10. so 


Me 


iH 


H 


14 


4,261 


9.70 


Vi 


l3/i 


Me 


12 


2.683 


9.20 


Me 


^Vi 


H 


12 


2,249 


9.10 


5.^ 


x% 


iHe 


10 


1,31s 


9.00 


M 


2 


iMe 


10 


1,013 


8.80 


^i 


2H 


iMe 


9 


858 


8.80 


I 


2l/^ 


iH 


9 


617 


8.80 


x\^ 


23/4 


iH 


9 


S16 


8.80 


iH 


3 


x% 


9 


403 


9.00 


iH 


3V4 


iH 


8 


320 


9.00 


iH 


35'^ 


l^yi 


8 


278 


9.20 


iH 


3M 


m 


8 


247 


9.20 


l3/4 


4 


iH 


8 


224 


9-So • 


I^i 


4i/i 


2 


8 


200 


9.50 


2 


45^ 


2}i 


8 


180 


9- SO 



In ordering, always specify size of bolt. 




Fig. 42. 
Showing Lock Washer on Bolt. 

When the nut is screwed upon the bolt, it first strikes the rib on the 
lock washer, which, being harder than the nut, progressively upsets 
and forces some of the metal of the nut into the thread of the bolt, 
thereby preventing the nut from backing off or loosening. 

Can be used on any make of bolt or nut. The same bolt, nut and lock 
washer can be used as often as required. 

Prices upon receipt of specifications. 



154 



Materials 




Fig. 43. 



The positive lock washer is so constructed that the "body" of the 
washer carries the load of compression and the tapered ends are thus 
relieved and the spring is constant. The barbs, being free to move when 
subjected to vibration, force themselves deeply into the nut and metal 
backing. 

Are reversible and can be used many times. Do not injure the nut, 
its thread, or the threads of the bolt. 



Machine Bolts 



155 



Machine Bolts 

Approximate Weight per ioo or Machine Bolts with Square 
Heads and Square Nuts 



Yi 


Me 


% 


Pound 


Pound 


Pound 


2.55 


4-4 


7.71 


2.64 


4.65 


8.04 


2.73 


4.9 


8.36 


2.9 


5.4 


9.01 


3.08 


5.9 


9.66 


3-43 


6.8 


10.94 


4-45 


7.8 


12.74 


5. 45 


8.7 


14-37 


6.46 


9-7 


15.83 


7.09 


10.7 


17-3 


7.7 


II. 7 


18.76 


8.3 


12.7 


20.2 


8.9 


13-7 


21.58 


9-5 


14.7 


22.95 


10.2 


15-7 


24.42 


10.8 


16.7 


25.9 


11-5 


17.7 


27.37 


12. 1 


18. 7 


28.84 


13.4 


20.8 


31.8 


14.6 


22.9 


34.75 


15.8 


24.9 


37.7 


17 


26.9 


40.65 


18.2 


28.9 


43.6 


19-4 


31.0 


46.55 


20.6 


33 


49-5 


21.8 


35 


52.45 


23 


37 


55.4 


24.2 


39 


58.35 


25.4 


41 


61.3 


26.6 


43 


64.25 


27.8 


45 


67.20 


29 


47 


70.15 


30.2 


49 


73.1 


31.4 


51 


76.05 


32.6 


S3 


79 


33.8 


55 


81.95 


35 


57 


84.9 


36.2 


59 


87.8 


37.4 


61 


90.75 


38.6 


63 


93-7 

1 



He 


i/i 


9/i6 


% 


Pound 


Pound 


Pound 


Pound 


10 








10.53 








11.03 


15-5 


■■i9;8" 


28.9s 


II. 9 


16.7 


21.6 


30.89 


12.8 


17.9 


23.4 


31.83 


14.5 


20.4 


27 


36.7 


17.25 


24.91 


31-5 


41.55 


18.75 


27.64 


33-1 


45.4 


20.90 


29-74 


36.7 


49.28 


23.09 


32.89 


40.3 


53.16 


25.27 


34-98 


43 


57.04 


27.50 


36.01 


47.3 


61.9 


29-59 


38.61 


50.9 


65.77 


31.68 


41.22 


52.9 


68.9 


33.9 


43.82 


56.5 


72.77 


35.73 


46.42 


60.7 


76.71 


37-56 


49.02 


64-3 


80.58 


39 


51.64 


67.9 


84.45 


43-18 


56.84 


75-1 


92.19 


47.36 


62.04 


82.3 


99-94 


51.6 


67.24 


89-5 


107.69 


55.-^6 


72.44 


96-7 


115-44 


59-92 


77.64' 


103.9 


123.19 


64.20 


82.84 


III. I 


130.94 


68.36 


88.04 


118. 3 


138.69 


72.52 


93.24 


125-5 


146.44 


76.68 


98.44 


132.7 


154-19 


80.84 


103.64 


139-9 


161.94 


85 


108.83 


147. 1 


169.69 


89.16 


114.04 


154.3 


177-44 


93-32 


119.20 


161. 5 


185-19 


97-48 


124.44 


168.7 


192.94 


lOI . 64 


129.6s 


175.9 


200.69 


105.80 


134.80 


183. 1 


208.44 


109.96 


140.04 


190.3 


216.19 


114. 12 


145-24 


197.5 


224.94 


118.28 


150.44 


204.7 


232.19 


122.44 


155.64 


211. 9 


240.44 


126.60 


160.84 


219. 1 


248.24 


130.76 


166.04 


226.3 


254.94 



156 



Materials 



Approximate Weight per ioo of Machine Bolts with Square 
Heads and Square Nuts — (Continued) 



Length 


H 


% 


I 


iH 


iH 


iH 


Pound 


Pound 


Pound 


Pounds 


Pounds 


Pounds 


H 














I 














47.63 












iH 


50.10 












iH 


52.57 


81.25 










3 


57.6 


90.63 


. 137.50 


178.00 


235.37 




2H 


63.44 


98.63 


149.10 


192.87 


253.75 




3 


69.84 


106.3 


160.75 


207.7s 


272.12 


'"'458" 


3H 


75.93 


114.30 


171.55 


222.62 


290.50 


483 


4 


81.77 


122.30 


182.35 


237.50 


308.88 


508 


4W 


87.61 


130.30 


193.15 


252.38 


327.2s 


533 


S 


93. 45 


138.30 


203.90 


267.2s 


345.62 


558 


sH 


99.46 


146.30 


214.75 


282.13 


364-00 


583 


6 


105.13 


154.30 


225.65 


297.00 


382.37 


608 


\6H 


III. 14 


162.30 


236.35 


311 -87 


399.22 


633 


7 


117. 15 


170.30 


247.15 


316.7s 


416.07 


658 


7H 


123.16 


178.30 


257.95 


321.62 


432.92 


683 


8 


129.17 


186.30 


268.75 


336.49 


449-77 


708 


9 


141. 19 


202.30 


290.3s 


366.23 


483.47 


758 


lo 


153.21 


218.30 


311.95 


395.98 


517.17 


808 


II 


165.23 


234.30 


333. 55 


425.73 


550.87 


858 


13 


177.25 


250.30 


355.15 


455.48 


584-57 


908 


13 


189.27 


266.30 


376.75 


485.33 


618.27 


958 


14 


201.29 


282.30 


398.35 


514.98 


651.97 


1008 


IS 


213.31 


298.30 


419.9s 


544.73 


685.67 


1058 


i6 


225.33 


314.30 


441.55 


574.48 


719.37 


1108 


17 


237.35 


330.30 


463.15 


604.23 


753.07 


IIS8 


i8 


249.37 


346.30 


484.75 


633.98 


786.77 


1208 


19 


361.39 


362.30 


506.35 


663.73 


610.47 


1358 


20 


273.41 


378.30 


527.95 


693.48 


844.17 


1308 


31 


285.43 


394.30 


549-55 


723.23 


877.17 


1358 


32 


297-45 


410.30 


571. 15 


752.98 


911.57 


1408 


33 


309.47 


426.30 


592-75 


782.73 


945.27 


I4S8 


34 


321.49 


442.30 


614.35 


812.48 


978.97 


1508 


35 


333.51 


458.30 


635.9s 


842.23 


1012.67 


1558 


36 


345.53 


464.30 


657.55 


871.98 


1046.37 


1608 


37 


357.55' 


480.30 


679.15 


901.73 


1080.07 


1658 


38 


369.57 


496.30 


700.75 


931.48 


1113.77 


1708 


29 


381.59 


512. 30 


722.35 


961.23 


1147.47 


1758 


30 


393.61 


528.30 


743.95 


990.98 


1181.17 


1808 



These weights are for bolts with bolt size nuts, and with heads of diameter equal 
to iH times diameter of bolt, and thickness equal to % times diameter of bolt. 



Machine Bolts 



157 



Machine Bolts with Square or Button Heads, Square Nuts 
AND Finished Points 

Adopted Sept. 20, 1899, to take effect Oct. i, 1899. List prices per 100. 

















Diameter, inches 










Length, — 
























inches 












%6 














Yi 


Me 


% 7/ 


ie 


¥2 


and 


% 


'A 


I 


iH 


iH 


1I/2 $1 


.70 $ 


2.00 


$2.40 $2 


80 


$3.60 


$5.20 


$7.20 


$10.50 


$15.10 


$22.50 


$30.00 


2 I 


.78 


2.12 


2 


.56 3 


00 


3.86 


5. 58 


7.70 


11.20 


16.00 


23.70 


31. so 


21^ I 


.86 


2.24 


2 


.72 3 


20 


4.12 


5. 96 


8.20 


11.90 


16.90 


24.90 


33.00 


3 I 


■ 94 


2.36 


2 


.88 3 


40 


4.38 


6.34 


8.70 


12.60 


17.80 


26.10 


34-50 


zVi 2 


.02 


2.48 


3 


.04 3 


60 


4.64 


6.72 


9.20 


13.30 


18.70 


27.30 


36.00 


4 2 


.10 


2.60 


3 


.20 3 


80 


4.90 


7.10 


9- 70 


14.00 


19.60 


28.50 


37. so 


4K2 2 


.18 


2.72 


3 


.36 4 


00 


5.16 


7.48 


10.20 


14.70 


20.50 


29.70 


39.00 


5 2 


.26 


2.84 


3 


.52 4 


20 


5.42 


7.86 


10.70 


15.40 


21.40 


30.90 


40.50 


53^ 2 


.34 


2.96 


3 


68 4 


40 


-5.68 


8.24 


11.20 


16.10 


22.30 


32.10 


42.00 


6 2 


.42 


3.08 


3 


84 4 


60 


5.94 


8.62 


11.70 


16.80 


23.20 


33.30 


43. SO 


m 2 


.50 


3.20 


4 


00 4 


80 


6.20 


9.00 


12.20 


17.50 


24.10 


34.50 


45.00 


7 2 


.58 


3-32 


4 


16 5 


00 


6.46 


9.38 


12.70 


18.20 


25.00 


35.70 


46. SO 


7!/^ 2 


.66 


3-44 


4 


32 5 


20 


6.72 


9.76 


13.20 


18.90 


25.90 


36.90 


48.00 


8 2 


.74 . 


J.S6 


4 


48 5 


40 


6.98 


10.14 


13.70 


19.60 


26.80 


38.10 


49. SO 


9 2 


.90 > 


3.80 


4 


80 5. 


80 


7.50 


10.90 


14.70 


21.00 


28.60 


40.50 


52.50 


10 3 


.06 


^04 


5 


12 6 


20 


8.02 


11.66 


15.70 


22.40 


30.40 


42.90 


55.50 


II 3 


.22 ^ 


t.28 


5 


44 6 


60 


8.54 


12.42 


16.70 


23.80 


32.20 


45 30 


58.50 


12 3 


.38 


^52 


5 


76 7. 


00 


9.06 


13.18 


17.70 


25.20 


34.00 


47.70 


61.50 


13 






6 


08 7. 


40 


958 


13.94 


18.70 


26.60 


35.80 


50.10 


64.50 


14 








6 


40 7- 


80 


10.10 


14.70 


19.70 


28.00 


37.60 


52.50 


67.50 


IS 








6 


72 8. 


20 


10.62 


15.46 


20.70 


29.40 


39 40 


54.90 


70.50 


16 








7 


04 8. 


60 


II. 14 


16.22 


21.70 


30.80 


41.20 


57.30 


73.50 


17 








7 


2,(> 9- 


00 


11.66 


16.98 


22.70 


32.20 


43.00 


59.70 


76.50 


18 








7 


68 9- 


40 


12.18 


17.74 


23.70 


33.60 


44.80 


62.10 


79.50 


19 








8 


00 9. 


80 


12.70 


18.50 


24.70 


3500 


46.60 


64.50 


82.50 


20 








8 


32 10. 


20 


13.22 


19.26 


25.70 


36.40 


48.40 


66.90 


85.50 


21 














13.74 


20.02 


26.70 


37.80 


50.20 


69.30 


88.50 


22 














14.26 


20.78 


27.70 


39.20 


52.00 


71.70 


91.50 


23 














14.78 


21.54 


28.70 


40.60 


53.80 


74.10 


94.50 


24 














15.30 


22.30 


29.70 


42.00 


55.60 


76.50 


97. SO 


25 














15.82 


23.06 


30.70 


43.40 


57.40 


78.90 


100.50 


26 


















31.70 


44.80 


59.20 


81.30 


103.50 


27 


















32.70 


46.20 


61.00 


83.70 


106.50 


28 


















33.70 


47.60 


62.80 


86.10 


109.50 


29 
















.... 


34.70 


49.00 


64.60 


88.50 


112.50 


30' 


















35.70 


50.40 


66.40 


90.90 


115.50 



Bolts with hexagon heads or hexagon nuts, 10 per cent advance. 

If both hexagon heads and hexagon nuts, 20 per cent advance. 

Machine bolts with countersunk head, joint bolts with oblong nuts, bolts with 
tee heads, askew heads, and eccentric heads, 10 per cent advance. 

Bolts with cube heads, 20 per cent advance. 

Bolts requiring extra upsets to form the head, 20 per cent advance for each extra 
upset. 

Special bolts with irregular threads and unusual dimensions of heads or nuts will 
be charged extra at the discretion of the manufacturer. 

Bolts with cotter pin hole, prices upon application. In ordering bolts with cotter 
pin hole, state size of hole, and distance from end of bolt to center of hole. 



158 



Materials 




Bolt Ends and Lag Screws 

Bolt Ends Fitted with Square Nuts* 

Adopted Jan. 30, 1895, to take effect Feb. 14, 1895. 
List prices per pound. 




Fig. 44. 










Fig 


•45. 


Size of 
iron, 
inches 


Length, 
inches 


Length 

of thread, 

inches 


Price per 
pound 


Size of 
iron, 
inches 


Length, 
inches 


Length 

of thread, 

inches 


Price 

per 

pound 


Me 


6 


I 


$0.20 


x\^ 


13 


4H 


$0.10 


% 


7 


iH 


.18 


xM 


14 


5 


.11 


Me 


7 


1K2 


.16 


x% 


15 


sV^ 


.11 


^ 


8 


2H 


.14 


m 


16 


6 


.11 


H 


9 


3 


.12 


1% 


17 


6H 


.12 


H 


10 


3H 


.10 


1% 


18 


7 


.12 


n 


II 


ZV2 


.10 


m 


19 


7^ 


.12 


I 


12 


4 


.10 


2 


20 


8 


.12 



* With hexagon nuts, 10 per cent advance. 

Prices of bolt ends shorter than above standard lengths will be quoted upon appli- 
cation. 



Weights of Nuts and Bolt Heads in Pounds 



159 



Coach Screws with * Square or Washer Heads; Gimlet Points 

List prices per 100, 





Diameter, inches 


Length, 


Yi 








Yis 








inches 


and 
Me 


% 


7/6 


1/^ 


and 

5/8 


% 


li 


I 


1I/2 


$2.25 


$2.70 


$3.15 


$3.75 










2 


2.45 


2.96 


3-47 


4. II 


$6.00 








2K2 


2.6s 


3.22 


3.79 


4.47 


6.50 


$9.20 






3 


2.85 


3.48 


4. II 


4.83 


7.00 


9.90 


$15.00 




sH 


3.0s 


3.74 


4.43 


5.19 


7.50 


10.60 


16.00 


$22.00 


4 


3.25 


4.00 


4.7s 


5.55 


8.00 


11.30 


17.00 


23.30 


4K2 


3.45 


4.26 


5.07 


5.91 


8. SO 


12.00 


18.00 


24.60 


5 


3.65 


4.52 


5.39 


,6.27 


9.00 


12.70 


19.00 


25.90 


S'A 


3.85 


4.78 


5.71 


6.63 


950 


13.40 


20.00 


27.20 


6 


4.05 


5. 04 


6.03 


6.99 


10.00 


14.10 


21.00 


28.50 


61/2 






6.35 


7.35 


10.50 


14.80 


22.00 


29.80 


7 






6.67 


7.71 


11.00 


15.50 


23.00 


31.10 


7^ 






6.99 


8.07 


11.50 


16.20 


24.00 


32.40 


8 






7.31 


8.43 


12.00 


16.90 


25.00 


33.70 


9 






7.95 


9. IS 


13.00 


18.30 


27.00 


36.30 


10 








9.87 


14.00 


19.70 


29.00 


38.90 


II 








10.59 


15.00 


21.10 


31.00 


41.50 


12 








II. 31 


16.00 


22.50 


33.00 


44.10 



* Coach screws with hexagon and tee heads, 10 per cent advance. 



Weights of Nuts and Bolt Heads in Pounds. Kent 

For calculating the weight of long bolts. 



Diameter of bolt, in inches 

Weight of hexagon nut and head 

Weight of square nut and head 




.017 
.021 


.057 
.069 


1/ 

.128 

.164 


.267 
.320 


.43 
■ 55 


.73 

.88 




I 

1. 10 
1. 31 


iH 

2.14 

2.56 


3.78 
4.42 


1% 

5.6 
7.0 


2 

8.75 
10.50 


2H 
17 
21 


3 


Weight of hexagon nut and head 

Weight of square nut and head 


28.8 
36.4 



i6o 



Materials 



to (N O 






%5 



<o o <r) t- 









^^SiS^S isa^g K^a^S 








1"^^ o j:5^<^^5^^£i>;;5^ 







.gcg ^8 R^i2^^l?^^e=^K 






^S-^JfJ^^^^f^JJ^S^^^^^ 





2 2 8 2^a^^8^ i!?^ft8 i2g 




??J^^^°2S"?5??^^^g't^?:^^ 



t2 


^ 


^ 


8 


i2 


S 


s^ 


fttg 


^ 


o 


^ 


^ 


^ 


2 


^ 


H 


00 


o» 


o 


2 


M 


N 


M 


^ 


i? 


l> 


^ 


h" 


8 


- 


r^ 



i?^i;?&^^ 8 a^R^s ^R^S 




ovovoo t^r-oooo 0>0^0 M w cs rO'* 





^^^a^^^i;?2^!$ir?^ag 






inioioio"Ovo<^t^oooo o^o o i-i N 







a 



J??>K 8 ^?^&Ji?^^^RJ^S 








^"^•^loioioioovo t^oooo o>a> 









o oiooiomoioo>oo o o 

rofO"^'4-4'4iOiO<OtO I>l>od 



fO ro ro ro ro •^ ■* 



lo lo "O vd 



ro CO 00 fO 



N N pi fOrororO'<i-'i-'4 



Q ^ 






c«N(N<NrorororO-^ 






1-2 

< 



Cap Screws 



i6i 




Fig. 46. 



On all screws of one inch and less in diameter, and less than four inches 
long, threads are cut f of the length. Beyond four inches, threads are 
cut half the length. 

Regular cap screws are soft and have ground heads. Special prices 
on black heads, extra finished and case hardened screws. 

Cap screws with over-sized heads take the list of regular cap screws 
with the same-sized heads. 

Price of steel screws will be 25 per cent above the price of iron. 



l62 



Materials 
Drop-Forged Turn-Buckles 



Without Stubs 



With Stubs 
Fig. 47. 

With right and left U. S. Standard thread. 
List prices with and without stubs. 



Diameter of 
stub, inches 


Inside opening 

of buckle, 

inches 


Length over all 

(including 
stubs), inches 


Each 


M 


3 


14 


$0.36 


Me 


3 


14 


.38 


% 


5 


19K2 


.40 


^16 


5 


19^2 


.42 


\^ 


6 


21 


.45 


Vi 


9 


24 


.56 


9/16 


6 


22 


.48 


^A 


6 


23 


.50 


% 


9 


26 


.63 


% 


6 


23 


.63 


% 


9 


26 


-79 


'A 


6 


23 


.75 


n 


9 


26 


• 94 


I 


6 


23 


.88 


I 


9 


26 


I. ID 


iH 


6 


24 


I. GO 


iH 


9 


27 


1.25 


iH 


6 


25 


1.25 


m 


9 


28 


1.56 


m 


6 


26 


1.38 


iH 


9 


29 


1.73 


iH 


6 


26 


I. SO 


m 


9 


29 


1.88 


iH 


6 


26 


1.75 


m 


6 


27 


2.00 


iii 


6 


28 


2.25 


2 


6 


29 


2.65 



Drop-Forged Turn-Buckles 



163 



Drop-Forged Turn-Buckles 



With One Eye and On? Hook 

n 



Wi'-th Two Eyes 



(^sai^^^^^gJjEs;:;;^^ 



With Two Hooks 

Fig. 48. 

With right and left U. S. Standard thread. 
List prices with either one hook and one eye, two eyes, or two hooks. 



Diameter 
of 


Inside opening of buckle, inches 




threaded 


































end, 
inches 


3 


5 


6 


9 


12 


IS 


18 


24 


36 


48 


72 


H 


$0.40 






















Me 


.45 






















% 




$0.6.=; 




















y% 






$0.72 


$0.85 


$0.95 


$1.15 












v% 






.80 


• 95 


1.05 


1.30 


Si. 55 


$2.05 








% 






1. 10 


1.25 


1. 00 


1.70 


2.00 


2.65 








% 






1. 35 


1-55 


1.70 


2.10 


2.45 


3.20 








I 






1.65 


1.85 


2.0s 


2. so 


2.9s 


3.80 


$4.25 






^\i 






2.10 


2.35 


2.55 


3.0s 


3.55 


4.55 


5.0s 






iH 






2.65 


2.9s 


3.2s 


3.90 


4. SO 


5.75 


6.40 


$8.90 




^% 






3.15 


3.45 


3.80 


4.50 


5.20 


6.60 


7.2s 


10.00 




i^ 






3.70 


4.05 


4.4s 


5.20 


5. 95 


7-45 


8.20 


11.20 


$14.20 


iH 






4.6s 




5.50 


6.40 


7-25 


9.00 


9.90 


13.40 


16.90 


134 






5. 30 




6.40 


7.40 


8.40 


10.40 


11.40 


15.40 


19.40 


x% 






6.50 




7.60 


8.75 


9.«5 


12.10 


13.25 


17.7s 


22.25 


2 






7-75 




9.10 


10.40 


11.75 


14.40 


15.75 


21.00 


26.30 



164 



Materials 




P 


ftftftftftS 
SSftSSooo|oo 

10 10 lO >0 10 N 


•* 


'■'.'.'.'.'.'.'.'. -^ So 


i 


:::::::: :ftft 

: ; :' : : ! : ; :"^ 






::::::::: 8 8 


::::::::: "^ ^ 


"r^ 




::::::::: ftft 






n 


:::::: 8 8 8 88 


: : : : : :j!?ft"^^^ 


i 


:::::: ^8ftft8 


: : : : : :^^?55^ 




: : =2 8 8 ^^ 8 8 88 


: : t^ l^-S^ f^"S J^i^'ft 




: :S8 ^2 a Sftftft 


: :2 J?If?^g^^S;t;^ 


IN 


^8 2 8a.c8^ 8 8 8 8 


^ «= 2 2 J? Ji? ^ ?5 'S ;^ ^ 


;^ 


i2{C^8i2ft8 8 ftfta 


^^^-^^t^^i^f^a??^^ 




2 8^8^8^8888 


^ *-«> 2 G Si?^ S 5r"S 


"S- 


^i?i^8^a^ 8ftftft 


>rnO t^OiO w fOOoO rrjfO 


- 


eg ftR 8 ^.8 88888 


rtiovoooa. cs ■sJ-VO oo» 


1 


;^k^;s^i^#^|js:^;I 



Thumb Screws 165 

Thumb Screws, Drop-Forged Steel, Threaded, U.S. Standard 



Fig. so. 

Can be furnished in styles A to F. 
List prices per loo. 



Diameter, 
inches 


1/^ 


3/1 6 


H 


Me 


,« 


7/16 


H 


?i6 


% 


% 


Threads 






















per inch 


40 


24 


20 


18 


16 


14 


13 


12 


II 


10 




r ^4 


S3. 20 


$3.6 


3 $4-10 


$4. 80 


I5.90 














^! 


3.40 


3.8 


D 4 


30 


5-00 


6.10 


$7.60 


$9.50 


$11.70 








M 


3.60 


4.CX 


D 4 


50 


S.20 


6.40 


8.00 


10.00 


12.40 






S 


I 


3.80 


4.2 


3 4 


70 


5. 50 


6.80 


8. SO 


10.60 


13.10 


$16.00 


$23.10 


-s 


iH 


4.00 


4-4 


3 4 


90 


5.80 


7.20 


9.00 


11.20 


13.80 


16.80 


24.40 


.s 


ii^ 


4.20 


4.6 


3 5 


10 


6.20 


7.6c 


9.50 


11.90 


14.60 


17.80 


25.80 


"S 


13/4 




4.8 


3 5 


40 


6.60 


8.10 


10.10 


12.60 


15.50 


18.80 


27.20 


1' 


2 






S.o 


3 5 


70 


7.00 


8.60 


10.70 


13.30 


16.40 


19.90 


28.60 


2H 








6 


10 


7.40 


9.20 


11.40 


14.10 


17.30 


21.00 


30.10 


2I/2 










6 


SO 


7.90 


9.80 


12.10 


14.90 


18.30 


22.10 


31.60 


§ 


2% 










6 


90 


8.40 


10.40 


12.80 


15.80 


19.30 


23.30 


33.10 


J3 


3 










7 


40 


8.90 


11.00 


13.50 


16.70 


20.30 


24.50 


34.70 


ft 


3H 














10.00 


12.30 


15.10 


18.50 


22.50 


27.00 


38.10 


J 


4 














11.20 


13.80 


16.90 


20.50 


24.80 


29.70 


41.50 


4'A 
















15.40 


18.70 


22.70 


27.40 


32.70 


45. 20 




5 
















17.00 


20.70 


25.20 


30.. 30 


36.00 


49.60 




sVi 
















18.80 


22.90 


27.80 


33.30 


39.60 


54.30 




.6 




















30.40 


36.60 


43.60 


60.00 



i66 



Materials 



Round Head Iron Rivets 

Approximate number in one pound. 











Diameter of 


wire 










Length, 
























inches 
































3/i 





Me 


I 


2 


3 


Yi 


4 


S 


6 
154 


Me 
188 


7 
221 


8 
256 


9 


% 




















334 


H 


32 


42 


SI 


57 


65" 


75 


80 


89' 


108 


131 


■IS9 


18S 


215 


278 


. H 


29 


37 


45 


SO 


57 


67 


70 


78 


94 


114 


138 


158 


185 


238 


% 


26 


33 


41 


45 


51 


59 


63 


70 


84 


lOI 


122 


139 


163 


208 


^ 


24 


30 


37 


41 


46 


54 


57 


63 


75 


91 


109 


123 


145 


185 


I 


22 


28 


34 


39 


42 


49 


52 


57 


68 


82 


98 


III 


131 


166 


iH 


20 


26 


31 


34 


39 


45 


47 


53 


63 


75 


90 


lOI 


119 


ISI 


iH 


19 


24 


29 


32 


36 


42 


44 


49 


58 


69 


83 


93 


109 


138 


l3/i 


18 


22 


27 


29 


33 


39 


41 


45 


54 


64 


76 


86 


lOI 


127 


IH 


17 


21 


25 


28 


31 


37 


38 


42 


SI 


59 


71 


80 


94 


119 


13/4 


IS 


18 


22 


24 


27 


33 


34 


40 


44 


55 


63 


70 


82 


104 


2 


13 


17 


20 


22 


25 


29 


30 


35 


40 


47 


S6 


62 


73 


92 


2H 


12 


IS 


18 


19 


22 


27 


28 


32 


36 


42 


50 


56 


66 


83 


2>^ 


II 


14 


17 


18 


20 


24 


25 


29 


33 


39 


46 


50 


60 


75 


23/i 


10 


13 


IS 


17 


19 


22 


23 


26 


30 


36 


42 


46 


55 


67 


3 


9 


12 


14 


IS 


17 


21 


22 


24 


28 


33 


39 


43 


51 


64 


3H 


81^ 


II 


13 


14 


16 


19 


20 


23 


26 


31 


36 


40 


47 


59 


3>^ 


8 


loi/^ 


12 


laVi 


IS 


18 


19 


21 


24 


29 


34 


38 


44 


55 


334 


7Vi 


93/4 


II3/4 


123/4 


14 


17 


18 


20 


23 


27 


32 


35 


41 


52 


4 


7H 


9H 


II 


12 


13 


16 


17 


18 


21 


25 


30 


33 


38 


49 


4H 


7 


83/4 


loi/^ 


iiH 


123/4 


15 


16 


17 


20 


24 










4^ 


6^^ 


81/4 


10 


I03/4 


12 


14 


15 


16 


19 


23 










4% 


614 


8 


9H 


10 


IlH 


133/4 


143/4 


IS3/4 


18 


22 










5 


6 


7H 


9 


m 


II 


13 


14 


15 


17 


21 








•• 


SM 


53/4 


7I/4 


81/^ 


9M 


loi/^ 


12^ 


13H 


T-AVi 


16^ 


20 










5H 


SH 


7 


8/4 


9 


10 


12 


13 


14 


16 


19 










5% 


5H 


63/4 


73/4 


m 


9\^ 


IlH 


12H 


I3i/i 


IS 


18 








.. 


6 


5 


6H 


7^ 


m 


9% 


II 


12 


13 


14 


17 











3}^ cents per pound, net. 



Dimensions of Standard Wrot Pipe 



167 



Dimensions of Standard Wrot Pipe 



12 

'it 


3. 
II 


gT3 


u 


2 


< 


Ins. 


Ins. 


H 


.269 


H 


.364 


H 


.493 


H 


.622 


H 


.824 


I 


1.047 


iM 


1.38 


ii/i 


1. 61 


2 


2.067 


2l/4 


2.467 


3 


3.066 


3^^ 


3.548 


4 


4.026 


45'^ 


4.508 


5 


5. 045 


6 


6.065 


7 


7.023 


8 


7.981 


9 


8.937 


10 


10.018 


II 


II 


12 


12 


13 


13.2s 


14 


14.25 


IS 


15.25 


16 


16.25 


17 


17.25 


18 


18.25 


19 


19.2s 


20 


20.25 



r 



.405 


.54 
.675 
.84 


I. OS 


1. 315 
1.66 


1.90 


2.375 
2.875 


3.50 


4.00 


4.50 


S.oo 


5.563 
6.625 
7.625 
8.625 
9.625 


10. 75 


11-75 


12.75 


14 


IS 
16 


17 
18 


19 


20 


21 



Ins. 

H + H2 

11/16 
M6+H2 

iMe 

iMe 

iii/ie 

iiMe 

2% 

2% 

3I/2 

4- 

4V2 

5 

5^/1 6 

m 

10% 

11% 

12% 

14 
15 
16 
17 
18 
19 





X. 


'rt 






Q.'O 







,., <U 1) 






G 


i 


•o.S 
a3 <o 


l-^-i 


-S 


§ 
X3X1 




^ 


JD 0. 


"S ° 


*(=! 


"S 


feTj'o. 


.a 

XI 




.ii§ 





0^ 


1 i ° 




A 


0^ 




P. 


si 








Ins. 






.068 


27 


.334 


21/64 


.19 


•393 




088 


18 


.433 


7/16 


.29 


.522 




091 


18 


.567 


?i6 


.3 


.658 




109 


-14 


.701 


11/16 


• 39 


• 815 




113 


14 


.911 


2%2 


•4 


1.025 




134 


iii/^ 


1. 144 


15^2 


• SI 


1.283 




140 


111/2 


1.488 


1I542 


.54 


1.627 




145 


111/2 


1.727 


l23/^2 


.55 


1.866 




154 


iii/i 


2.2 


27/^2 


•58 


2.339 




204 


8 


2.62 


2% 


• 89 


2.82 




217 


8 


3.24 


3/4 


• 95 


3.441 




226 


8 


3.738 


32%2 


I 


3.938 




237 


8 


4.233 


4W 


1.05 


4.434 




246 


8 


4.733 


4% 


I.I 


4.931 




259 


8 


5.289 


5%2 


1. 16 


5.489 




280 


8 


6.347 


61^2 


1.26 


6.547 




301 


8 


7.34 


71 H2 


1.36 


7.54 




322 


8 


8.332 


81 H2 


1.46 


8.534 




344 


8 


9.324 


9% 


1.56 


9.527 




366 


8 


10.445 


10^16 


1.68 


10.645 




375 


8 


11.439 


II!/l6 


1.80 


11.639 




375 


8 


12.433 


1227/64 


1.90 


12.633 




375 


8 


13.675 


13* %4 


1.98 


13.875 




375 


8 


14.668 


142 H2 


2.15 


14.869 




375 


8 


15.662 


152 H2 


2.21 


15.863 




375 


8 


16.656 


I62H2 


2.30 


16.856 




375 


8 


17.65 


172^2 


2.40 


17.8s 




375 


8 


18.644 


1841/64 


2.50 


18.844 




375 


8 


19.637 


195/i 


2.59 


19-837 




375 


8 


20.631 


20^i 


2.72 


20.831 






.27 

•36 

• 49 
.62 
.82 
I. OS 
1.38 
1. 61 
2.07 
2.47 
3.07 
3. 55 
4.07 
4. SI 
5. 04 
6.06 
7.02 
7.98 
8.93 
10.02 
II 
12 

13.25 
14.25 
15^25 
16.25 
17.2s 
18.2s 
19.25 
20.25 



Taper of conical tube ends % inch in diameter in 12 inches. 

Contributed by Louis H. Frick. No. 74, Extra Data Sheet, Machinery, October, 
1907. 

Seamless drawn brass and copper tubes are made by American 
Tube Works, Boston, Mass.; Ansonia Brass and Copper Co., Ansonia, 
Conn., office 19 and 21 Cliff St., New York; Benedict & Burnham Mfg. 
Co., Waterbury, Conn., office 13 Murray St., New York; Randolph & 
Clowes, Waterbury, Conn., and Bridgeport Brass Co., Bridgeport, 
Conn. The following sizes are kept in stock, in 12 feet lengths, by 
Merchant & Co., 517 Arch St., Philadelphia. The five columns signify 
as follows: 

A = outside diameter of tube in inches. 



i68 



Materials 



B = thickness of side by Stubs' (or Birmingham) gauge. When 
seamless tubes are ordered to gauge number, it is understood that this 
gauge is intended unless otherwise specified. 

C = thickness of sides of tube in decimals of an inch. 

D = weight, in pounds per lineal foot, of brass tube for columns A, 
B and C. (For copper, add one-nineteenth). 

Tubes will be furnished hard, unless ordered annealed or soft. 



A 


B 


c 


D 


A 


B 


C 


D 


A 


B 


C 


D 


H 


i8 


.049 


II 


1% 


13 


.095 


1.68 


2I/2 


12 


109 


3.02 


Me 


IS 


.049 


15 


1% 


II 


.120 


2.10 


2I/2 


10 


134 


3.68 


% 


17 


.058 


22 


1% 


15 


.072 


1.40 


2H 


14 


083 


2.44 


He 


17 


.058 


25 


1% 


14 


.083 


1. 61 


2% 


12 


109 


3.18 


H 


17 


.058 


29 


m 


13 


.095 


1.82 


2% 


10 


134 


3.87 


9/16 


17 


.058 


34 


m 


II 


.120 


2.27 


2H 


14 


083 


2.57 


H 


i6 


.06s 


42 


xli 


15 


.072 


I -50 


23/4 


12 


109 


3.37 


% 


i6 


.065 


51 


m 


14 


.083 


1.72 


23/4 


10 


134 


4.07 


''yi 


i6 


.065 


61 


m 


13 


.09s 


1.96 


2% 


12 


109 


3.50 


I 


i6 


.065 


70 


m 


II 


.120 


2.44 


2% 


10 


134 


4.26 


1% 


i6 


.065 


79 


2 


14 


.083 


1.84 


3 


10 


134 


4.46 


iH 


i6 


.065 


88 


2 


13 


.095 


2.10 


3H 


10 


134 


4.8s 


iH 


14 


.083 I 


12 


2 


10 


.134 


2.91 


3^/i 


10 


134 


5.24 


iH 


II 


.120 I 


57 


2^ 


14 


.083 


1.97 


Z% 


10 


134 


5. 62 


1% 


15 


.072 I 


08 


2}i 


13 


.095 


2.23 


4 


10 


134 


6.00 


m 


14 


.083 I 


25 


2H 


10 


.134 


3.10 


4H 


10 


134 


6.39 


x% 


11 


.120 I 


76 


2I/4 


14 


.083 


2.08 


AV2 


10 


134 


6.78 


iH 


IS 


.072 I 


19 


2l/4 


13 


.095 


2.38 


aH 


10 


134 


7.17 


iH 


14 


.083 I 


36 


2H 


10 


.134 


3.29 


5 


10 


134 


7.56 


iH 


13 


.095 I 


55 


2% 


14 


.083 


2.20 


5H 


10 


134 


7.94 


iH 


II 


.120 I 


92 


2% 


13 


.095 


2.51 


5!/^ 


10 


134 


8.33 


iH 


15 


.072 I 


29 


2% 


10 


.134 


3.49 


5M 


10 


134 


8.72 


iH 


14 


.083 I 


48 


2H 


14 


.083 


2.33 


6 


10 


134 


9. II 



Merchant & Co. supply sizes up to 7 inches outside or inside diameter, 
and up to 16 inches inside diameter, of other gauges as well as those given 
in the table; also tubes of special shapes, such as square, triangular, 
octagonal, etc. ; and bronze tubes. 

They also have in stock, in lengths of 12 feet, the following sizes of 
seamless brass and copper tubing, made of same outside diameter as 
standard sizes of iron piping, so as to be used with the same fittings as 
the iron pipe. 

A = nominal inside diameter of iron pipe, in inches. For actual 
inside diameters. 

B = outside diameter of iron pipe and of seamless tube, in inches. 

C = inside diameter of seamless tube, in inches. 

D = weight per foot of brass pipe. cols. B ajod C. For copper, add 
one-nineteenth. 



Tin and Zinc 



169 



A 


B 


c 


D 


A 


S 


C 


£> 


A 


B 


C 


D 


% 


1^2 


H 


.28 


% 


iHe 


2%2 


1.15 


2 


2% 


2M« 


4.15 


H 


lji2 


11/^2 


.43 


I 


iMe 


I%2 


I. so 


2H 


2yi 


27l6 


4. SO 


% 


21.^2 


^%2 


.58 


iVI 


154 


IIH2 


2.25 


3 


?,\^ 


3M6 


8.00 


Vi 


1^6 


% 


.80 


11/2 


l7/i 


Il%2 


2.55 


4 


Wi 


4H 


12.24 



TIN AND ZINC 

The pure metal is called block tin. — When perfectly pure (which 
it rarely is, being purposely adulterated, frequently to a large proportion, 
with the cheaper metals lead or zinc), its specific gravity is 7.29; and its 
weight per cubic foot is 455 pounds. It is sufi&ciently malleable to be 
beaten into tin foil, only Hooo of an inch thick. Its tensile strength is 
but about 4600 pounds per square inch; or about 7000 pounds when made 
into wire. It melts at the moderate temperature of 442° F. Pure block 
tin is not used for common building purposes; but thin plates of sheet 
iron covered with it on both sides constitute the tinned plates, or, as they 
are called, the tin, used for covering roofs, rain pipes and many domestic 
utensils. For roofs it is laid on boards. 

The sheets of tin, are united as shown in this Fig. First, several 
sheets are joined together in the shop, end for end, as at tt, by being first 
bent over, then hammered 
flat, and then soldered. 
These are then formed into 
a roll to be carried to the 
roof, a roll being long 
enough to reach from the 
peak to the eaves. Dif- 




FiG. SI. 



ferent rolls being spread up and down the roof are then united along 
their sides by simply being bent as at a and s, by a tool for that purpose. 
The roofers call the bending at 5 a double groove, or double lock; arid the 
more simple ones at t, a single groove, or lock. 

To hold the tin securely to the sheeting boards, pieces of the tin 3 or 4 
inches long, by 2 inches wide, called cleats, are nailed to the boards at 
about every 18 inches along the joints of the rolls that are to be united, 
and are bent over with the double groove s. This will be understood 
from y, where the middle piece is the cleat, before being bent over. The 
nails should be 4-penny slating nails, which have broader heads than 
common ones. As they are not exposed to the weather, they may be of 
plain iron. 



1 70 Materials 

Much use is made of what is called leaded tin, or ternes, for roofing. 
It is simply sheet iron coated with lead, instead of the more costly metal 
tin. It is not as durable as the tinned sheets, but is somewhat cheaper. 

The best plates, both for tinning and for ternes, are made of charcoal 
iron, which, being tough, bears bending better. Coke is used for 
cheaper plates, but inferior as regards bending. In giving orders, it is 
important to specify whether charcoal plates or coke ones are required; 
also whether tinned plates, or ternes. 

Tinned and leaded sheets of Bessemer and other cheap steel are now 
much used. They are sold at about the price of charcoal tin and terne 
plates. 

There are also in use for roofing, certain compound metals which resist 
tarnish better than either lead, tin, or zinc but which are so fusible as to 
be liable to be melted by large burning cinders falling on the roof from a 
neighboring conflagration. 

A roof covered with tin or other metal should, if possible. Slope not 
much less than five degrees, or about an inch to a foot; and at the eaves 
there should be a sudden fall into the rain-gutter, to prevent rain from 
backing up so as to overtop the double-groove joint s, and thus cause 
leaks. When coal is used for fuel, tin roofs should receive two coats of 
paint when first put up, and a coat at every 2 or 3 years after. Where 
wood only is used, this is not necessary; and a tin roof, with a good pitch, 
will last 20 or 30 years. 

Two good workmen can put on, and paint outside, from 250 to 300 
square feet of tin roof, per day of 8 hours. 

Tinned iron plates are sold by the box. These boxes, unUke glass, have 
not equal areas of contents. They may be designated or ordered either 
by their names or sizes. Many makers, however, have their private 
brands in addition; and some of these have a much higher reputation 
than others. 



Sizes and Weights of Lead Pipes 
Sizes and Weights of Lead Pipes 



171 



Inner 
diameter, 


Thickness, 


Weight per 


Inner 
diameter. 


Thickness, 


Weight per 


inches 


inches 


foot, ounces 


inches 


inches 


foot, pounds 


% 


.08 


.10 
Pounds 


i3^ 


.14 


3.5 


% 


.12 


1. 00 


ii/^ 


.17 


4.2s 


% 


.16 


1. 25 


lYi 


• 19 


5.00 


% 


■ 19 


1-5 


11/2 


.23 


6.5 


H 


.09 


.75 


iH 


.27 


8.0 


Yi 


.11 


I.O 


m 


.13 


4.0 


Vi 


.13 


1.25 - 


x% 


■ 17 


S.o 


Vi 


.16 


1.75 


m 


.21 


6.5 


Vi. 


• 19 


2.0 


m 


.27 


8.5 


H 


.25 


3.0 


2 


.15 


4.75 


54 


.09 


1.0 


2 


.18 


6.0 


5i 


.13 


1.5 


2 


.22 


7.0 


^ 


.16 


2.0 


2 


.27 


9.0 


% 


.20 


2.5 


2l/i 


3/16 


8.0 


% 


.22 


2.75 


2H 


1/4 


II. 


H 


.25 


3-5 


2I/2 


Me 


14.0 


H 


.10 


1.25 


2H 


3/i 


17.0 


% 


.12 


1.75 


3 


3/i6 


9.0 


% 


.16 


2.25 


3 


H 


12.0 


% 


.20 


3.0 


3 


Me 


16.0 


% 


.23 


3-5 


3 


% 


20.0 


% 


.30 


4.75 


3\i 


3/16 


9.5 


I 


.11 


2.0 


3H 


H 


iS.o 


I 


.14 


2.5 


35/2 


Me 


18.S 


I 


.17 


3.25 


3I/2 


% 


22.0 


I 


.21 


4.0 


4 


Me 


12. 5 


I 


.24 


4-75 


4 


H 


16.0 


m 


.10 


2.0 


4 


Me 


21.0 


iH 


.12 


2.5 


4 


% 


25.0 


iH 


.14 


3.0 


4M 


Me 


14.0 


iH 


.16 


3-75 


4H 


H 


18.0 


iH 


.19 


4.75 


5 


M 


20.0 


iH 


.25 


6.00 


5 


% 


31.0 



172 



Materials 



K--x^ k-A->| 




1 1 -i^;. 

•>lN|<-o4---af> 



. 8 

c 


^, 


Vl- -^ -«^ -<«-#> X-* S*« ^ X-* Nf* 

^x rex t-(X 1-.X rnx rex »-.x f-<x rex ..^ 


^ 




H^ 


rex sjo mx spo vr- sj* sw vpi rex NflO v^ 


^ 




ts 


spO-,,)lv<lOv(IOx-*NP)s50sp» S« V* 

-ix ,-.x rex t^x «x ,jx _hX «x rex mx 


^ 


fO(^<^>0^>0000>0 o o o 



<D CO to to 

i-<X V* lOX N^ ~x-. USX v^ s^ fix se« x* 



i-<x Nrf lox V!* NT- >nN. v^ sr- rex vpi Xj!< 
rt rex rt ^x ojx rt a>x c<Sx „ -ix rK 

M M M N Ol M ro -"^ rl- VO "O 



*><0 Ntf5 N^ (D Ntf> v^ -^J* NO 

,-,X KX ^X spO v-" OJ"X NX N^ vpO NflO vfO S(-i 

M •• m .-•X lox M £4 NX rex u5x ,-x tix 



v-.spO—XvflOvr-'sjJisSO vpOx-*^^vS" 

oix lox ^ tOv P.K r-fx icx reX reX r-ix .-^x 



tt> N^ NSC s(0 <e N^ vjo • 



M l-l i-H W M 



»-hX NPO NflO Sjf N^-t V 



V-< N^ N^ nP^ WS 
rnX ,-iX U5X r-ix ^ 



M IN ro CO 



. i-N st-« spa s^ 
CO t-(N NX reN. 






2~"rt^; 



v* x-i sF< rex -.^ vpo 

- rex rex r-«x ^ ,-.x i^x 

M M (N ts ro fO 



CS N N (N 



I s^ to N50 N^ vJD sp V* 

. NX Sr-- rex NX U3X NX Nja* ,mX 
Cq OSn «3 „ re IN .-hX rf 

wwuMMNcoro 



I NFS ^ 

I vpq ,-«x S50 rex \rS- 



N IN cq ro'oo °?0 



.ox r^x ( 



(N PJ PO fO fO •n- 



^ NSO NSO to NSO 

rex se>i nn ^x v-- »ox n^o v^ 

-IN -Tn lo „ NX ,(1 ^X ,-X 






to --fO to CO nW N^ 

. v-i ^N v-i vpq v-t NpO rex 05X 
lOX _i NX «X 0>X lOX M ^ 



H N ro "S- <0 



O N VO O 



::S^:5;; 



W ro t 10«0 00 O 



Chains and Cables 



173 



Chains and Cables 

(United States Navy Standard.) 














Load in 


pounds 


A 


B 


c 


D 


Pounds per 














foot 


Ultimate 


Working 


Inches 


Inches 


Inches 


Inches 








H 


^/i 


iMe 


25/32 


.875 


3,360 


670 , 


5/16 


iHe 


1I/2 


2%2 


1. 000 


5,040 


1,000 


H 


iH 


l3/4 


31/^2 


1.70 


7,280 


1,460 


^6 


l3/i 


2M6 


I%2 


2.00 


10,080 


2,020 


^ 


iiHe 


2?^ 


IIH2 


2.50 


13,440 


2.690 


9i6 


l7/i 


25/i- 


Il%2 


3.20 


16,800 


3,360 


H 


2M6 


3 


l2 3/^2 


4.125 


20,720 


4,140 


iMe 


2l/i 


31/4 


. I2%2 


S.co 


25,200 


5,040 


M 


2^ 


3}^ 


13^2 


5.875 


30,240 


6,050 


1%6 


2IH6 


3% 


23/^2 


6.70 


35,280 


7.060 


% 


2ji 


4 


27/^2 


8.00 


40,880 


8,180 


1^6 


3M6 


4% 


215/^2 


9.00 


47,040 


9,410 


I 


3H 


4% 


2l%2 


10.70 


53,760 


10,750 


iMe 


39i6 


4% 


22 %2 


11.20 


60,480 


12,100 


iH 


3% 


5H 


22 %2 


12.50 


68,320 


13,660 


1^6 


3li 


5%^ 


3542 


13.70 


76,160 


15,230 


iH 


4H 


5% 


3%2 


16.00 


84,000 


17,000 


iHe 


4% 


6H 


315/^2 


16.50 


91,840 


18,400 


iH 


49i6 


6% 


35i 


18.40 


101,360 


20,300 


i^a 


4% 


61 He 


325/^2 


19.70 


109,760 


21,900 


i^ 


5 


7 


33^2 


21.70 


120,960 


24,200 



174 



Materials 



Chain End Link and Narrow Shackle 





(U.S. Navy 
Standard) 






Standard Hexagonal Nut 
and Head. 



Fig. 54. 



A 


Ai 


B 


C 


D 


E 


F 


G 


H 


7 


K 


L 


M 


N 





Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


Ins. 


%6 


^ie 


1% 


3H 


2^^ 


H 


1 1/6 


34 fi 


iH 


-lU 


34 fi 


o3,^ 


o3^ 






H 


2H6 


M 




3/ 


1/6 


3/6 


ii/ 


13/ 


3/6 


25/ 


27/ 






% 


11/16 


21/ 


4% 


3 


I 


17/ 6 


H 


2 


l7/ 


3/6 


3 


33/ 






iMe 


34 


2V^ 


454 


31/ 


I 


17/ 6 


1/ 


2 


17/ 


3/6 


M 


35/ 






¥i 


1^6 


2IM6 


5 


3I/ 


IH 


i^ie 


H 


21/ 


2I/ 


3/fp 


zH 


4 






1%6 


% 


2% 


5I4 


3% 


IH 


i^ie 


Me 


21/ 


21-^ 


34 P 


3% 


4I/ 






% 


I 


31/ 


53/ 


4H 


ll/ 


1II/6 


5/6 


21/ 


23/ 


1/ 


41/ 


45/ 


5/ 


3^ 


15/16 


1M6 


39/6 


6 


43/ 


ll/ 


iii/e 


5/6 


21/ 


23/ 


1/ 


4H 


.■> 


5/ 


3H 


I 


iH 


33/ 


65,^ 


45/i 


II/ 


2/6 


3/ 


3 


23/ 


1/ 


47/ 


.S3/ 


5/ 


37/ 


iMe 


l3/6 


37/i 


6% 


aU 


ll/ 


21/ 6 


3/ 


3 


23/ 


H 


5 


5H 


5/i 


4 


iH 


ii/4 


4H 


7^ 


51/ 


l3/ 


25/16 


7/6 


31/ 


31/ 


5/6 


51/ 


6 


3/ 


4^ 


13/16 


l5/l6 


43/ 


73/ 


53/ 


13/ 


25/6 


Vie 


31/ 


31/ 


5/6 


53/ 


61/ 


3/ 


4H 


T% 


1% 


49/6 


81/ 


53/ 


1% 


27/6 


7/6 


33/ 


31/ 


5/6 


6 


65/ 


3/ 


4^ 


iMe 


l7/l6 


43/ 


83/ 


5% 


l7/ 


27/6 


1/ 


33/ 


31/ 


5/6 


61/ 


63/ 


3/ 


47/ 


l3/i 


iH 


5 


83/ 


6I4 


2 


211/6 


1/ 


4 


31/ 


5/6 


61/ 


7H 


7/ 


5H 


lM6 


iri6 


53/6 


9 


61/ 


2 


211/ 6 


1/ 


4 


31/ 


5/6 


63/ 


73/ 


7/ 


5^ 


I^ 


iH 


5'A 


95/ 


67/ 


2I4 


3I/6 


9/6 


41/ 


4 


3/ 


7 


73/ 


7/ 


sH 


1^6 


iiHe 


5% 


9% 


71/ 


21/ 


3I/6 


ri6 


41/ 


4 


3/ 


7H 


8 


7/ 


sH 


iH 


l3/i 


5IM6 


loi/ 


73/ 


21/ 


37/6 


5/ 


5 


41/ 


3/ 


71/ 


81/ 




6H 


iiHe 


113/6 


6 


10% 


73/ 


21/ 


37/6 


5/ 


S 


41/ 


3/ 


73/ 


83/ 




6H 


l3/4 


174 


61/ 


11% 


8 


23/ 


31 1/6 


11/6 


51/ 


5 


7/6 


8 


qi/ 




6H 


113/16 


115/6 


6^i6 


Il5/ 


81/ 


23/ 


311/ 6 


11/6 


5H 


5 


7/6 


81/ 


03/ 




6H 


1^4 


2 


61 He 


Il3/ 


81/ 


23/ 


3IM6 


11/6 


51/ 


5 


7/6 


8H 


95/ 


ll/ 


6H 


115/16 


2M6 


61-^ 


12 


83/ 


23/ 


311/6 


11/6 


51/ 


5 


7/6 


83/ 


9% 


iH 


6% 



No. 33. Supplement to Machinery, June, 1904. 



Table for Eye Bolts 



175 



Table for Eye Bolts 

(Contributed by H. A. H.) 







^_„^^ 




r^ 




^ 


TJ 


a 




^ 


^ 








'£ 




i 


c 

B 


■a 

II 






w 




w 




rt 
^ 
M 


n 


1^ 

3 






hi 












-^•b 
•^^ 








Fig. 55- 




XI 


|co 


cl 














S 


^ 


2h 
















12; 


+J 




A 


B 


c 


D 


E 


F 


G 




M 


C/3 


.375 


2 


.75 


.625 


.1875 


• 375 


.25 


16 


677 


750 


• 5 


2.125 


I 


.75 


.25 


.5 


.3125 


13 


1,257 


1,172 


.625 


2.25 


1-25 


I 


.3125 


.625 


.4375 


II 


2,018 


2,296 


.75 


2.375 


I • 4375 


1. 125 


.3125 


.6875 


.5 


10 


3,020 


3.000 


.875 


2.5 


1.6875 


1-375 


.375 


.75 


.625 


9 


4,194 


4,687 


I 


2.75 


1.87s 


1. 5 


.4875 


.875 


.75 


8 


5,509 


6,750 


1. 125 


2.87s 


2.125 


1.62s 


.5 


I 


.8125 


7 


6,931 


7,921 


1.25 


3 


2.375 


1.75 


.5 


1. 125 


.875 


7 


8.899 


9.188 


1.375 


3.125 


2.625 


1.875 


.5625 


I. 1875 


I 


6 


10,541 


12,000 


1.5 


3.25 


2.75 


2 


.625 


1.25 


1.0625 


6 


12,938 


13,546 


1.625 


3.375 


3 


2.125 


.6825 


1.375 


1. 125 


5.5 


15,149 


15,187 


1.75 


3.5 


3.2s 


2.25 


.75 


i-S 


1.25 


5 


17,441 


i8,7So 


1.875 


3.62s 


3.5 


2.375 


.8125 


1.62s 


1.312s 


5 


20,490 


20,671 


2 


3.75 


3.75 


2.5 


.875 


1-75 


1.375 


4.5 


23,001 


22.686 



176 



Materials 



Sprocket Wheels for Ordinary Link Chains 







R=4- 



Section E-F. 
Pitch Chain Sheave. 



« "= ^ (Hutfe Pag. 502-1) B 




'^~\^ 

Section 
A-B. 



Fig. 56. 



Sprocket Wheels for Ordinary Link Chains 



177 







?% 


Sfx^^;^^:;^.2.2.2.2.2^^2 :::::: 


H 


|:;"iif^j|:g:s:s^.:s:s:s^:s:sifff 


«> 




1 

a 
.2 



•a 
II 


^^S"ft&^ S;S J^lCS ^<5?J?^^ : : 


2 2 2 C'^'S^ ^ S'^J(??^^g'jqS5^ : : 


^ 




8 S^'RSa^^^-S'S^C^cS^^bf;; : : 


2 2 S S ;:rt?J:8 ^ ^^^^^^^ ^^% : : 


1/2 




C^K-^-g-S ^?:?^S^SSf:?u t?>g^ . 


0>0>OHrO'*tOO^Oi-(!Nroioy3>-ifOi/10 • 
i-iMHwiHMCNiM(N(N!NCSrOroi^^ • 


^ 




ss^^^^^8>gj"€??JJ?^^^^s^s;^ 


««>2S22>^&^a^?3S?^S'.f?,?5P5^ 


ro 


5d 


g'S'f^^^^J^^^S Fl'Rcg^Si^ ^S"^ 


°=«'^2S2^'2J:'2S^RSS!^g'f^!i5<^ 


IN 




VD<0<0 VJOUO-^-^rOM 0) N M M c?ioo r^iO'l- 
t-^t^odoio'i-i roiovD i>-odod M 4<Oo6 pi 10 


- 


a. 

2 

So 


S'S'S.^^^t^^^&^^^iS^J^^^^S.:^ 


t-t^t-00 OiO P) •^•^lOVO 1^00 0-. P^ '^O C^P» 





a. 


000000>H-lO^Ol-lOl-ll-liHI-il-lWMI-HM 

-*-^M 5 l>vO MOOVO '^TP) OOOIOOO '^O P^O 


'£>'£> t^oOOO C?iM p] rOTfio<OvO t>0 PI '*l>0^ 


o> 


^0 
°o 


-^■^^ s ?^=§ s:;^^ ^ ?i !5 J^^'^ 8 <^ s,.g 


iO>/1<OI>t~OOOMPlPIPOtiiDir>OOOMrfU3 


00 


M 
W 


j?n?{^^'§fis?Ts.^a<!?g>n?ti§!^^f: 


loioioo t^ooo M p^ P) roTfo j>a^iH po 


t^ 


M 


ae>^5'^'&se3%^fifT^^g^3>'s^ 


■<*-rruoio<o<£> t^ooo M w P) -*ioo a>o 


VO 





^^^^f?)cg?^KJ??2^R2"S5^'^5!^ 


n<r)rfTti/)u-jvoj>ooooo%cno m <r!^<oi> 


m 


^0 

00 


^ ^^f ^S S> ^ 3. ?:^ J2 ^ ^^% ^ ?3 ^^ 


fCrcro-^'^'^io^'O l^l>oooooo M PI roio 


II 

1 
6 


e 

-a 
c 


ll 


to to to 
^-^ HWMMMMPip^pqPtrOfOrorcifCTfioio 


II "o 


hHi-iMWP«P)cqNrOfOf<)';f-*-:f^iOO<Ot-t^ 


II 


|j|:?::I;^^;si^";^?^^'^;^2" ^:g^;g:si|: 



178 



Materials 



« ^ ;§i ;S il^ ;i^ :s: :s: s s :$: 5: 5: :s: 






^ 



J? 


% 




°cO 


^ 


■'^ 




fo 



» M 


as8 


??s 


7^S ■ . . 








o» 0^ 


f^ fj-s-s 




























<g^ 


§ri 










•* -tt 


















00 00 


a.?? 


^?r 






































^^ 


"S^ 




S^a? : : 








l> t^ 


8 ?5 


^^a 


P>y:i^^ : : 








R a 


;^e> 


^s 


2 ^]^g^ . 








M M 


M ?3 


^j? 


9>^%%^- : 








-ft^SR 


{^^ 


^j?a ^^^ 


: 






■ 





•o <o 


^ a 


s ^^ ^^^^^ 














M l-H 


^s>?i 5? 


00 00 00 00 00 00 












g'g' 


a s 


g S"^^^^^?? 


10 










J> Ol 


^s 


'S 9>P>Pi%% 


^ 








5SS 




j^s. 


fo w CM» <0 ^ 


^ 




"* Tj-VD 00 


as; 


^^^P,^% 


^ 


% 




ss 


f:J^ 


ST? 


^^^)^9>^ 


<2"ft 




■* Tl- 


M m" 


M C3 


n'^^P>^Y^% 


^ 




%% 


^^ 


^& 


^J^^Sgi'^ 


fj 


00 




fO re 


\rno 


^ a 


J^'S^ 9>^^ 


J^*^ 




12 i2 


^% 


:?.^ 


PsftS^^-SSg 


■^ 


^ 


•c^ - ■ • • 


2 2 


Tj- ly^ 


t^ a\ 


?J J?5T^ ^f^ 


^ 


^ 


^ I ; : I 


M M 


^'S 


^"2 


S^SP^f^S' 


eg 


fo 


•^ : : : : 


M M 


rO >rnO 00 


?5 ^^^T's a, 


fo 


p? 


^ ; ; ; ; 


'S- Tl- 


S.'^ 


^S 


? s^c^'a R 


S" 


r~ 


??,<s . . . 



1 



N-^lOt^ON-^lOt^OOOl-ll^ 

MtHl-ll-l(N<N(NNN(NnrOrO 



J3 

II 






.2 J3 

II " 



wMMMMMNC^MrrjPOroPO-cfTrioifl 



C CCN «\ c*v ^X ^X tOx ^N «X CCX «\ «X COX rnX ^X W^ t~X 



Transmission or Standing Cables 



179 



Pliable Hoisting Rope 

With 6 strands of 19 wires each. 



Trade 




Cir- 
cum- 


Weight 
per foot 


Breaking 

strain in 

tons of 2000 


Proper 

working 

load in 

tons of 2000 


Circumfer- 
ence of 
Manila 
rope of 


Minimum 

size of 

drum or 

sheave in 

feet 


num- 


eter 


ference 


with 


pounds 


pounds 


equal 


ber 




in 
inches 


hemp 
center 


" 




strength 




Iron 


Steel 


Iron 


Steel 


Iron 


Steel 


Iron 


Steel 


I 


2H 


6H 


8.00 


74.0 


155.0 


15.0 


31.0 


14.0 




13.0 


8.5 


2 


2 


6.0 


6.3 


65.0 


125.0 


13.0 


25.0 


13.0 




12.0 


8.0 


3 


1% 


5.5 


5.25 


54.0 


106.0 


II. 


21.0 


12.0 




10. 


7.25 


4 


M 


S.o 


4.10 


44.0 


86.0 


9.0 


17.0 


II. 


15.0 


8.5 


6.25 


5 


m 


4.75 


3.6s 


39.0 


77.0 


8.0 


iS.o 


10. 


14.0 


7.5 


5. 75 


5l^ 


1% 


4.38 


3.00 


33.0 


63.0 


6.5 


12.0 


9.5 


13.0 


7.0 


55 


6 


iH 


4.0 


2.5 


27.0 


52. 


5.5 


10. 


8.5 


12.0 


6.5 


5.0 


7 


iH 


3-5 


2.0 


20.0 


42.0 


4.0 


8.0 


7.5 


II. 


6.0 


4.5 


8 


1 


3.13 


1. 58 


16.0 


33.0 


3.0 


6.0 


6.5 


9.5 


5.25 


4.0 


9 


% 


2.75 


1.20 


11.5 


25.0 


2.5 


5.0 


5.5 


8.5 


4.5 


3.5 


ID 


% 


2.25 


0.88 


8.64 


18.0 


1.75 


3.5 


4.75 


7.0 


4.0 


3.0 


loH 


H 


2.0 


0.60 


5.13 


12.0 


1.25 


2.5 


3.75 


5.75 


3.5 


2.25 


loi^ 


?i6 


1.63 


0.44 


4.27 


9.0 


0.75 


1.5 


3.5 


5.0 


2.75 


1.75 


loH 


H 


1.5 


0.35 


3.48 


7.0 


0.5 


i.o 


3.0 


4.5 


2.25 


1.5 


loa 


7/16 


1.38 


0.29 


3.00 


5.5 


0.38 


0.75 


2.7 


3.75 


2.0 


1. 25 


lov.^ 


% 


1. 25 


0.26 


2.50 


4.5 


0.2s 


0.5 


2.5 


3.5 


1. 5 


1.0 



Transmission or Standing Cables 

With 6 strands of 7 wires each. 



IX 


1.5 


4.63 


3.37 


36.0 


62.0 


9.0 


13.0 


lo.o 


13.0 


13.0 


8.5 


12 


1.38 


4.25 


2.77 


30.0 


52.0 


7.5 


10. 


9.0 


12.0 


12.0 


8.0 


13 


1.25 


3.75 


2.28 


25.0 


44.0 


6.25 


9.0 


8.5 


II. 


10.75 


7.25 


14 


1. 13 


3.37 


1.82 


20.0 


36.0 


S.o 


7.5 


7-5 


10. 


9.5 


6.25 


15 


1.0 


3.0 


1.5 


16.0 


30.0 


4.0 


6.0 


6.5 


9.0 


8.5 


5.75 


16 


0.88 


2.62 


1. 12 


12.3 


22.0 


3.0 


4.5 


5.75 


8.0 


7.5 


5.0 


17 


0.75 


2.38 


0.88 


8.8 


17.0 


2.25 


3.5 


4.75 


7.0 


6.75 


4.5 


18 


0.69 


2.13 


0.70 


7.6 


14.0 


2.0 


3.0 


4.5 


6.0 


6.0 


4.0 


19 


0.63 


1.88 


0.57 


5.8 


II. 


1.5 


2.25 


4.0 


5.5 


5.25 


3.5 


20 


0.56 


1.63 


0.41 


4.1 


8.0 


1.0 


1.75 


3.25 


4.75 


4.5 


3.0 


21 


0.5 


1.38 


0.31 


2.83 


6.0 


0.75 


1.5 


2.75 


4.0 


4.0 


2.5 


22 


0.44 


1.25 


0.23 


2.13 


4.5 


0.50 


1.25 


2.5 


3.5 


3.25 


2.25 


23 


0.38 


1. 13 


0.9 


1.65 


4.0 




1.0 


2.25 


3.25 


2.75 


2.0 


24 


0.31 


1.0 


16 


1.38 


3.0 




0.75 


2.0 


2.75 


2.5 


1.75 


25 


0.28 


0.88 


0.T3 


1.03 


2.0 




0.5 


1. 75 


2.25 


2.25 


1.5 



i8o 



Materials 



loco f ion for Afax/'mum Mom en f. 



^ t 



1 i II 



-Oh- 



^-^--•fltfJ- 



CS denofes center of span, 

Ca cfenofes cenfer of ffrayfft/ of /oads, 

fV/j denotes hea^/es f /oad od/acenf fo CG. 

Let yY= fofaf /oad and //- moment. 

For M a maximum p/ace CS midrvai/ 
bettveen tV/, and CG and f/nd M under 
W/,. Forreacf/ons, /?/- ^^ and /?r' 
iV- Ri. For maximum moment /■f-f^i 
0/,-(i%Z,ty*iiB), ors/nce Dc'Df,. M' 
"^-(mi/t^Vzlz). 



Iwo yVhee/s Equa// i / Loacfecf. 




tfre/oad 



For B'or exceeds a S3S8L, y/= ^• 
and Rr'T^^rtj). 



Notation: /ill ya/aes in/ncfjes andpounds. 
kit =■ to fa/ /oad. >^ - /oad on one nr/>ee/. 
L ' /engrf/7 of span. B - tynee/ l/ase. 
Rl'/effreacf/on, /fr'r/^nfreacf/on. 
^' yerf/ca/ shear Teacf/'on nearest fo 
the point under considerafion. 
Of distance to front /yhee/ ) 
Or = distance to rear rvhee/ > ! 
coming on from the /eff, fff/ 'fnomenf 
under front tvheet, one ^hee/ on tfie spafi. 
fifs "moment under front tvhee/ nifh both 
ivtiee/s on fhe span. /^/-/ ~ /nomenf under rear 
trheel, one yyheel on the Span. Mrz - niomenf 
under rear fvheet, both tfhee/s on the span. 
CC" ya/ue of Or for ffrz a maximum. 
M- maximum moment. Z'-seciion modu/t>S. 
Si, 'Stress due fo bencf/ncf. 

Mrz- ^''(L-Dr -§) For yalues of 3 /ess than 
O.S8S8L, cC'i-^ and M' ^ (/-£ f. 

For t>oth yyhee/s on the span, f^'Z (^^'^r-f) 



Jyvo IVhee/ s Equalti / Loac/ec/, Ob//< ;/t/e ffeac//'o/7. 



..^ Notation: Same asaboye m'th addition of ; a 'Oncf/e of the reaction 

"■^»s.^^^ mth beam. A" cross secfionat area of beam. T' thrust or 

-(^^-^^^^•^yg pull due to oblique reaction. S" direct s/ress cfue to T 
- -— • — - -- - — ^"^^ (tension or compression). 

■ T^CDrfj), or r'f(Drf^)cota 
^'i'mi(Ortih or S'^COrr§)cofa. 
Afe, /*2, JC, M end 4> - same aS abot^e. 

, . - _ W , (Drt-'/zB)cotcx . Dr(L-Dr~''^BK 

ot 51,' i_ ( 2 -t- — 2r ' ' 

S*St,'a maximum ivhen Df • ^ *^ k - i' in^ot a-f-^ -J. 
~For light y/eifft?t I- beams f' about 3 depth of beany' 




Figs. 57, 58, 59. 



Modulus of Elasticity i8i 

Modulus of Elasticity 

The modulus of elasticity of any body is the ratio, within the elastic 
limit, of the stress per unit of area to the stretch per unit of length. 

Let S = stress per square inch, and 

L = elongation per unit of length. 

S' = total stress. 

L' = total elongation. 

O = original length. 

A — area of cross section in square inches. 

E = modulus of elasticity. 

Then E = j, which is found to be practically constant, and is a 

measure of the resistance which a body can oppose to change of shape. 

S' 

-J = S = stress per square inch, (i) 

A. 

u 

jr = L = elongation per unit of length 

Hence the modulus of elasticity is equal to the total stress, multiplied 
by the original length, divided by the area in square inches, multiplied 
by the total elongation. 



From equation (2), 


















S' = 


EL'A 

: 




(3) 


and since 
















!- 


and 


V 
= 


= L, then S = 


EL; 


(4) 


or the stress \ 


per unit of 


area 


is equal to the modulus multipUed by 


the 


elongation per unit of length. 










From (3), 


















V 


S'O 
EA 


SO 
E 




(5) 


and 




L 


5. 






(6) 



or the elongation per unit of length equals the stress per unit of area 
divided by the modulus. 



l82 



Materials 



Table of Moduli of Elasticity and of Elastic Limits for 
Different Materials 

The values here given are approximate averages compiled from many sottrces. 
Authorities differ considerably in their data on this subject. 



Material 



Modulus or 
coefliciency 
of elasticity 



Stretch or compression 

in a length of lo feet, 

under a load of 



looo lbs. per 
sq. in. 



I ton per 
sq. in. 



Ash 

Beech 

Birch 

•Brass, cast . . 
Brass wire... 

Chestnut 

Copper, cast. 
Copper wire . 

Elm 

Glass 



Iron, cast 



Iron, cast, average 

Iron, wrought, in either bars, 



sheets or plates . 



Iron bars, sheets, average. 

Iron wire, hard 

Iron wire ropes 

Larch 

Lead, sheet 

Lead wire 

Mahogany 



Oak. 



Oak, average 

Pine, white or yellow. 

Slate 

Spruce 



Steel bars . 



Steel bars, average. 

Sycamore 

Teak 

Tin, cast 



Lbs. per 
sq. in. 
1,600,000 
1,300,000 
1,400,000 

9,200,0C0 

14,200,000 
1,000,000 
18,000,000 
18,000,000 
1,000,000 
8,000,000 
12,000,000 

to 
23,000,000 
17.500,000 
18,000,000 

to 
40,000,000 
29,000,000 
26,000,000 
15,000,000 
1,100,000 
720,000 
1,000,000 
1 ,400,000 
1,000,000 

to 
2,000,000 
1,500,000 
1,600,000 
14,500,000 
1,600,000 
29,000,000 

to 
42,000,000 
35,500,000 

1,000,000 

2,000,000 
4,600,000 



Ins. 

.075 
.092 
.086 
• 013 
.009 
.120 
.007 
.007 
.120 
.015 
.010 
to 

.005 

.007 
.006 
to 
.003 
.004 
.005 
.008 
.109 
.167 
.120 
.086 
.120 
to 
.060 
.080 
•075 
.008 
.075 
.004 
to 
.003 
.003 
.120 
.060 
.026 



Ins. 

.168 
.207 
.192 
.029 
.019 
.269 
.015 
.015 
.269 
.034 
.022 

to 
.012 
.015 
.015 

to 
.007 
.009 
.010 
.018 
.244 



.192 
.269 
to 

.134 

.179 
.168 
.018 
.168 

.009 
to 
.006 
.007 



Table of Deflections 



183 



Table of Deflections 

The formulae are based on the assumption that the increase of deflec- 
tion is proportional to the increase of load. 
The values of the letters in the table are as follows: 

d = deflection of beam in inches. 
W — weight of extraneous load in pounds. 
w = weight of clear span of beam in pounds. 
/ = clear span of beam in inches. 
E = modulus of elasticity in pounds per square inch. 
/ = moment of inertia of cross section of beam in inches. . 



Moduli 


OF 


Elasticity 


OJ 


Various Materials 


Materials 


Moduli 




9,170,000 
14,230,000 


Brass wire 


Copper 


15,000,000 to 18 000 000 


Lead 


1,000 000 


Tin cast 


4,600 000 




12,000,000 to 27,000,000 (?) 
22,000,000 to 29,000,000 
26,000,000 to 32 000 000 




Steel 


Marble 


25,000,000 


Slate 


14,500,000 


Glass 




Ash 




Beech 




Oak 


974,000 to 2,283,000 
1,119,000 to 3,117,000, 1,926,000 

306 000 


Pine, longleaf 


Walnut 















i84 



Materials 



S g -S .2 ^ g i^ 
pq -2 -Si ^ G 



S|=- 






'i' 




+ 




1 




? 








"i" 




►^ 
^ 


^ 




5 


+ 
^ 


^ 


t 


^ 


+ 




























































rO 


H 


CO 


H 


^ 


^ 


% 


M 


M 

^ 


H 



■r! cS 



pq j3 



1^ 11^ IIS lis 



lO 00 1/5 



IS 



113 IIS lia lla 



lla lis 
-Is -i« 




Modulus of Rupture 



i8S 



From the table, it is found that for beams of similar cross section and 
of same material, and within the elastic limit, the load and deflections 
(neglecting the weight of the beam itself) are as follows: 

Deflections Under Given Extraneous Loads 



With same span. 



With same span and breadth ... 

With same span and depth 

With same breadth and depth . . . 



Inversely as the breadths and as the cubes of 

the depths 
Inversely as the cubes of the depths 
Inversely as the breadths 
Directly as the cube of the span 



Extraneous Loads eor a Given Deflection 


With the same span 


Directly as the breadths and as the cubes of 


With the same span and breadth . 
With the same span and depth — 
With the same breadth and depth . 


the depths 
Directly as the cubes of the depths 
Directly as the breadth 
Inversely as the cubes of the spans 



Modulus of Rupture 

The modulus of rupture is the total resistance, in pounds per square 
inch, of the fibres of a beam farthest from the neutral axis; and is iS 
times the center breaking load in pounds, of a beam of the given material, 
I inch square by i foot span. The values of the modulus of rupture, 
which is usually denoted by "C," may be obtained from the following 
table of transverse strengths, by multiplying the values therein by i8. 

One-third part of any of these constants (except those for 
wrought iron and steel) may be taken in ordinary practice as about the 
average constant for the greatest center load within the elastic limit. The 
loads here given for wrought iron and steel are already the greatest 
within elastic limits. 

Transverse strengths, in pounds 



li 



II 



11 



WOODS 

Ash: 

English 

Amer. White (Traut.) 

Swamp 

Black 

Arbor VitcB, Amer 

Balsam, Canada 

Beech, Amer 

Birch: 

Amer. Black 

Amer. Yellow 

Cedar: 

Bermuda 

Guadaloupe 

Amer. White or Arbor 

Vitae 

Chestnut 

Elm: 

Amer. White 

Rock, Canada 

Hemlock 



650 
650 
400 
600 
250 
350 
850 

550 
850 

400 
600 

250 

450 

650 
800 
500 



Hickory: 

Amer 

Amer. Bitter nut 

Iron Wood, Canada , 

Locust , 

Lignum Vitce 

Larch 

Mahogany 

Mangrove: 

White 

Black 

Maple: 

B"lack 

Soft 

Oak- 
English 

Amer. White (by Traut.). . . 

Amer. Red, Black, Basket. 

Live 

Pine: 

Amer. White (by Traut.). . . 

Amer. Yellow* (by Traut.). 



800 
800 
600 
700 
650 
400 
750 

650 
SSO 

750 
750 

SSO 
600 
850 
600 

450 
500 



i86 



Materiak 



Transverse strengths, in pounds — (Continued) 



Pine: 

Amer. Pitch* (by Traut.) 

Georgia* 

Poplar 

Poon 

Spruce: 

(By Traut.).. 

Black 

Sycamore 

Tamarack 

Teak 

Walnut 

Willow 



Metals 

Brass 

Iron, cast: 

1500 to 2700, average 

Common pig 

Castings from pig 

Employed in our tables 

For castings 2}^ or 3 ins. thick. . 
Iron, wrought, 1900 to 2600, average 

Wrought iron does not break; 
but at about the average of 2250 
pounds its elastic limit is reached. 
Steel, hammered or rolled; elas- 
ticity destroyed by 3000 to 7000. 

Under heavy loads hard steel 
snaps like cast iron , and soft steel 
bends like wrought iron. 

Stones, etc. 
Blue stone flagging, Hudson River. 
Brick: 

Common, 10 to 30, average 

Good Amer. pressed, 30 to 50, 

average 

Caen Stone 

Cement, Hydraulic: 

English Portland, artificial, 
7 days in water 

I year in water 

Portland, Kingston, N. Y., 7 
days in water 



550 
700 

450 
550' 
500 
400 
750 
550 
350 

850 

2100 
2000 
2300 
2025 
1800? 
2250 



30 



days 



Cement Hydraulic: 

Saylor's Portland, 7 
water 

Common U. S. cements, 7 
days in water 

The following hydraulic ce- 
ments were made into prisms, in 
vertical moulds, under a pressure 
of 32 pounds per square inch, and 
were kept in sea water for i year. 
Portland Cement, English, pure, 

I year old 

Roman Cement, Scotch, pure 

American Cements, pure, average 

about 

Granite: 

50 to 150, average 

Qtiincy 

Glass, Millville, New Jersey, 

thick flooring (by Traut.) 

Mortar: 

Of lime alone, 60 days old 

I measure of slacked lime in 
powder, i sand 

I measure of slacked lime in 

powder, 2 sand 

Marble: 

Italian, White. 

Manchester, Vt., White 

East Dorset, Vt., White 

Lee, Mass., White 

Montgomery Co., Pa., Gray. .. . 

Montgomery Co., Pa., Clouded. 

Rutland, Vt., Gray 

Glenn's Falls, N. Y., Black. . . . 

Baltimore, Md., White coarse. . . 

Oolites, 20 to 50 

Sandstones: 

20 to 70, average 

Red of Connecticut and New 

Jersey 

Slate, laid on its bed, 200 to 450, 

average 



100 
100 



170 
10 



116 

95 
III 

86 
103 
142 

70 
155 
102 

35 

45 

45 

32s 



Trautwine. 



Moment of Inertia 187 

Moment of Inertia 

The moment of inertia of the weight of a body, with respect to any 
axis, is the algebraic sum of the products obtained by multiplying the 
weight of each elementary particle by the square of its distance from 
the axis. 

If the moment of inertia with respect to any axis be denoted by /; the 
weight of any elementary particle by w; and its distance from the axis 
by r; the sum of all the particles by 2, then I = 'E(wr^). 

The moment of inertia of a rod or bar of uniform thickness, with 
respect to an axis perpendicular to the length of the rod, is 



=«'G+^ 



in which W equals the weight of rod, 2 I equals length and d equals the 
distance of the center of gravity of the section from the axis. 

For thin circular plates with the axis in its own plane, when r equals 
the radius of the plate. 

For circular plate, axis perpendicular to the plate. 

Circular ring, axis perpendicular to its own plane, 

r and / being the exterior and interior radii of the ring. 
Cylinder, axis perpendicular to the axis of the cylinder, 

r = radius of base and 2I — length of the cylinder. 

By making d equal to o in any of the above formulae, the moment of 
inertia for a parallel axis passing through the center of gravity is found. 

The term moment of inertia is also used in respect to areas, as the 
cross section of beams under strain. 

In this case, I = S(ar)2, in which a is the elementary area and r its 
distance from the center. 1 



i88 



Materials 























-5 I ^ 
















1 


] 














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>. 


>. 




1 
1 


§153 


£153 


^1 >~s 




tO| 00 


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=-15 


1 


1 




w| ro 


M| 00 


-l<§ 


-1^ 


+ 


ftnl a 




^\% 


=-1^ 


=^1^ 




Q 










as 








OhI^ 


fel^ 


c 
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-1^ 








1 M 


1 M 


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^1^ 


^1^ 


Sl^ 


51^ 


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O ^l^o 


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51^ 




u2 3 






















o 


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■ 


















6 


















1 


















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c3 
























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6 i 

a ° 










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H^ 














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'ro 






s; 






Ml 00 


Ml 00 
+ 

0, 


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M| 00 


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1 

1 ro 

> 


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Ml Tt 














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roi 00 






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go 


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rt . : 












































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a 

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a 
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5 

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rt 


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a 


5 § 


«'S 








OJ 


o 


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CJ 


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£ 


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Formulae for Transverse Strength of Beams 189 

Formulae for Transverse Strength of Beams 

P = load at middle. 

W = total load distributed uniformly. 

I = length, b = breadth, d = depth in inches. 
E = modulus of elasticity. 
R = stress per square inch of extreme fibre. 

/ = moment of inertia. 

C = distance between neutral axis and extreme fibre. 

For breaking load of circular section replace bd"^ by 0.59 d^. 

For good wrought iron the value of R is about 80,000; for steel about 
120,000. For cast iron the value of R varies greatly. Thurston found 
45,740 for No. 2 and 67,980 for No. i. 



190 



Materials 



General Formulae for Transverse Strength, Etc. 

The following table gives the values of W, etc., without introducing 
the modulus of elasticity or the moment of inertia. 



Formula for Round and Rectangular Solid Beams 









III 



5 so 



i 



^1? 



a 
.HI 



Sts 






Icvj 









^1 



^1 






r 



4!5 






11^ 






•til 



IP 



^N 

Jok 



lb 



5: 



5" r> 



>l< 






^1 



II 






•h 



On- 




f^ 



■-^ 



^ 



t^- 



^ 



_<3-t 



CHAPTER V 

ACCELERATION OF FALLING BODIES 

The change in velocity of a falling body which occurs in a unit of time 
is its acceleration. 

That due to gravity is 32.16 feet per second, in one second and is 
denoted by g. 

Let t = number of seconds during which a body falls. 

V = velocity acquired in feet per second at the expiration of 

t seconds. 
u = space fallen through in each second. 
h = total space fallen through in t seconds. 



Then 



gt = 32.16, t 



S.oiVh = 



2 2 2 g D4-32 



t = '- 



32.16 ▼ 8 V 



The table below gives the values of h, v and u, for values of t up to ten 
seconds. 





Space fallen 


Velocity 


Space fallen 


Time in . 


through in 


acquired in 


through in 


seconds. 


feet in 


feet per 


feet in 


t 


time t, 


second at end 


each second, 




h 


of time t, 

V 


M 


I 


16 


32 


16 


2 


64 


64 


48 


3 


145 


96 


80 


4 


257 


129 


113 


5 


402 


161 


145 


6 


580 


193 


177 


7 


789 


225 


209 


8 


1030 


257 


241 


9 


1303 


290 


273 


10 


1609 


322 


306 



191 



192 



Mechanics 



ISec 
3" 



\\ 



The graphical method of ascertaining the values of t, v, u and h is 
easily remembered and is often of service. 

In the triangle, Fig. 6i, let the vertical divisions on 
the left of the perpendicular represent the number of 
seconds through which the body falls = t. 

Let the base of each small triangle equal the velocity 
at the end of the first second = 32.16. Then the 
number of bases on each of the horizontal lines at 
I, 2, 3, etc., multiplied by 32.16 will equal the ac- 
quired velocity for the corresponding time = v. 

Let the area of each small triangle = 16.08. Then 
the number of such areas between o and any hori- 
zontal line multiplied by 16.08 will equal the height in feet fallen through 
in the number of seconds corresponding to that line = h. 

And the number of small triangles between each pair of horizontal 
lines, multiplied by 16.08 will equal the number of feet fallen through in 



^k 



Fig. 61. 



each second = u. 




Thus: 


/ = I, 2, 3, 4, 5, 6. 




V = 32.16 X I, 2, 3, 4, 5, 6. 




h = 16.08 X I, 4, 9, 16, 25, 36. 




u = 16.08 X I, 3, 5, 7, 9, II. 




Fig. 62. 



Parallelogram of Forces 

If two forces are applied to the same point, their resultant will be 
represented in intensity and direction by the diagonal of a parallelo- 
gram of which the adjacent sides represent the 
intensities and directions of the given forces. 

Let AB and AC represent, in intensity and 
direction, any two forces applied to the point 
A; then AD will correspondingly represent 
their resultant. 

Conversely, ii ADhe the known force acting at ^, it may be resolved 
into two components, in any direction in the same plane; which com- 
ponents will be the adjacent sides of a parallelogram having AD for its 
diagonal. 

Parallelopipedon of Forces 

If three forces, not in the same plane, act on the same point, they may 
be represented by the edges of a parallelopipedon and the diagonal 
through the point of application is their resultant. 



Height Corresponding to a. Given Acquired Velocity 193 
Height Corresponding to a Given Acquired Velocity 



Velocity. 


Height, 


Velocity, 


Height, 


Velocity, 


Height, 


V 


h 


V 


h 


V 


k 


Feet per 
second 


Feet 


Feet per 
secondr 


Feet 


Feet per 
second 


Feet 


.25 


.0010 


34 


17.9 


76 


89.8 


.50 


.0039 


35 


19.0 


77 


92.2 


.75 


.0087 


36 


20.1 


78 


94.6 


1. 00 


.016 


37 


21.3 


79 


97.0 


1. 25 


.024 


38 


22.4 


80 


99. 5 


1.50 


•035 


39 


23.6 


81 


102.0 


1.75 


.048 


40 


24.9 


82 


104.5 


2.0 


.062 


■ 41 


26.1 


83 


107. 1 


2.5 


.097 


42 


27.4 


84 


109.7 


3.0 


.140 


43 


28.7 


85 


112. 3 


3.5 


.190 


44 


30.1 


86 


iiS.o 


4.0 


.248 


45 


31.4 


87 


117. 7 


4.5 


.314 


46 


32.9 


88 


120.4 


5.0 


.388 


47 


34.3 


89 


123.2 


6.0 


.559 


. 48 


35.8 


90 


125.9 


7.0 


.761 


49 


37.3 


91 


128.7 


8.0 


.994 


50 


38.9 


92 


131. 6 


9.0 


1.26 


51 


40.4 


93 


134. 5 


lO.O 


1. 55 


52 


42.0 


94 


137.4 


II. 


1.88 


53 


43.7 


95 


140.3 


12.0 


2.24 


54 


45.3 


96 


143.3 


13.0 


2.62 


55 


47.0 


97 


146.0 


14.0 


3.04 


56 


48.8 


98 


149.0 


15.0 


3.49 


57 


50.5 


99 


152.0 


16.0 


3.98 


58 


52.3 


100 


15s 


17.0 


4.49 


59 


54.1 


105 


171. 


18.0 


5.03 


60 


56.0 


no 


188.0 


19.0 


5. 61 


61 


57.9 


115 


205.0 


20.0 


6.22 


62 


59.8 


120 


224.0 


21.0 


6.8s 


63 


61.7 


130 


263.0 


• 22.0 


7.52 


64 


63.7 


140 


304.0 


23.0 


8.21 


65 


65.7 


150 


3SO.O . 


24.0 


8.94 


66 


67.7 


175 


476.0 


25.0 


9.71 


67 


69.8 


200 


622.0 


26.0 


10. 5 


68 


71.9 


300 


1,399.0 


27.0 


11.3 


69 


74.0 


400 


2,488.0 


28.0 


12.2 


70 


76.2 


500 


3,887.0 


29.0 


13. 1 


71 


78.4 


■6a. 


5,597.0 


30.0 


14.0 


72 


80,6 


700 


7,618.0 


31.0 


14.9 


73 


82.9 


800 


9,952. 


32.0 


15.9 


74 


85.1 


900 


12.593.0 


33.0 


16.9 


75 


87.5 


1000 


15.547.0 



194 Mechanics 



The Lever 



The lever is a solid bar of any form, supported at a fixed point, about 
which it may turn freely. 

-^ -j The fixed point is the fulcrum. There are 

'^' "'pi three orders of levers. In those of the first 

order the points of application of the power 
^" and resistance are on opposite sides of the 

fulcrum. 

In the second order the resistance is ap- 
pKed between the fulcrum and the power. 

In the third order the power is apphed 
between the fulcrum and the resistance. 



± 



In any order ^^^- ^4- 

the weight W multiplied by the distance 
WF from the fulcrum must equal the 
power P multiplied by PF, to establish 
^^' ^' equilibrium. 

Whatever may be the shape of the lever, the power or resistance acts 
at the end of a hne drawn through the fulcrum and perpendicular to the 
line of direction of the power or resistance. This perpendicular is called 
the lever arm of its corresponding force, and the product of the lever arm 
and its force is called the moment of that force. When the moments are 
equal the forces are in equilibrium. 

If one moment exceeds the other, rotation will occur about the ful- 
crum in the direction of the force having the greater moment. 

The Wheel and Axle 

This is simply such an appUcation of the lever of the first order, that 
the power and resistance may act through greater distances; the radius 
of the wheel is the lever arm of the power and that of the drum the lever 
arm of the resistance. 

When the resistance is a weight, it will be raised if the moment of the 
power is the greater and vice versa. 

The Inclined Plane 

If a force P acts in the direction of C 
AB, to overcome the resistance R, then p 
P:R::a:b. "*" 

b a Fig. o6. 




Center of Gravity 1 95 

The Wedge 

The wedge is simply a double inclined plane, placed i- 

back to back. _t±iX^ 

If the force applied to "a wedge be represented by P t \ 
and the resistance to be overcome by R, the base of the 
wedge by a and its length by&;"then b 



P:R::a:b P = ^ and R = ^ 

a 



Fig. 67. 



Center of Gravity 

The center of gravity of a body is that point through which the effort 
of its weight always passes. If a body be suspended from any point, 
the direction of the hne of suspension will pass through its center of 
gravity. 

Therefore, the center of gravity of any body may be determined by 
finding the intersection of the hnes of suspension passing through points 
not on the same vertical hne. 

The center of gravity of two bodies is on a hne joining their respective 
centers of gravity and the distances from the center of gravity of either 
body to that of both of them (combined) are inversely proportional to 
the weights of the bodies respectively. 

To find the center of gravity of any irregular plane surface, divide it 
into triangles of any convenient areas. Find the center of gravity and 
the area of each triangle. Then assimiing any coordinate axes X and 
Y, multiply the area of each triangle by the abscissa of its center of gravity 
and divide the product by the sum of the areas of all the triangles. The 
quotient is the abscissa of the center of gravity of the entire figure. Find 
its ordinate in the same way; then the point determined by this abscissa 
and ordinate is the center of gravity of the figure. 

This method is precisely that shown by Fig. 61, Machinery Supplement 
No. 5. 

In addition to the formulae taken from Machinery Supplement No. 5, 
others are given as follows : 



Semiellipse 

The center of gravity of a semiellipse is on the semiaxis perpendiciilar 
to the base and at a distance from the base equal to the product of that 
semiaxis and the decimal 0.4244. 



196 Mechanics 

The Center of Gravity of Solids of Uniform Density 
Throughout 

Sphere and spheroid at center of the body. 

Hemisphere on the radius perpendicular to the base and at H its 
length from the base. 

Spherical Sector. — On the radius passing through the center of the 
circle cut from the sphere by the sector and at a distance from the center 
of the sphere, equal to three-fourths of the difference between the radius, 
and one-half the rise of the sector. Or G, representing the distance from 
center of sphere to center of gravity, R = radius of sphere and H the 

rise of the sector; then G = hIr j • 

Spherical Segment 

{2R- Hy 



G=% 



3R-H 



Spherical Zone 

Take the difference between the two segments whose difference is 
the zone. Find the center of gravity of each segment; then, by inverse 
proportion, find that of their difference. 

Frustrum of a Cone 

Let G = distance from base to center of gravity measured on 

the axis. 
A = area of large end. 
a = area of small end. 
H = height of frustrum measured on the axis. 



Then a = «fA+^^Aa + sa\ 

4 V ^ + VAa -\-a J 



The center of gravity of a paraboloid is on the axis and at a distance 
from the vertex equal to two-thirds that from vertex to base. 

A body suspended from center of gravity has no tendency to rotate. 

Center of gravity of regular figures is at geometrical center; of a triangle 
two-thirds distance from any angle to middle of opposite side; of semicircle 

on middle radius, 4244 r from center; of sector — r- from center; oi seg- 

3 ^ 

ment, from center (where c = chord and a = area); of cone or 

12 a 

pyramid, \i distance from center of base to apex a,. 02, az = areas of 
respective triangles. 

Center of gravity of two bodies, x = — 7-^^ 



Radius of Gyration 



197 



General formulae x 



aixi + (12X2 + azXz 
<Ji + <i2 + 0,3 

aiji + cgyi + azjz 
ai + a2 + az 




<vf 


^ 


O/ 

"^ 


\ 


\ 


~~-- 




\ 


<.x,- 


\--:f^ 




''^^\ 


c-Xj- 


T"!^- 


--^^_\^ 




^ 


^- 


^ 

















Y 



Fig. 69. 

Volume of a solid generated by the revolution of a surface about an axis 
in the same plane with it = area of the surface X circumference de- 
scribed by its center of gravity. 

Moment of Inertia 

Moment of inertia of rotating body = products of weights of particles 
X squares of distances from the axis = I = Wir^ + W2ri + Wzr^, etc. 
K'l, W2, etc. = weights of particles; Vi, Vi, etc. = distances from axis in 
same imits as the volumes of the particles of which weights are taken. 

Radius of Gyration 

Center of gjnration of rotating body is point at which weight itnay be 
assumed concentrated. Radius of gyration = k = distance from center 

of rotation to center of gyration. For circular disc, k = -^=. For 



circular ring, k 
1899.) 



-\/ 



r 



i?2 + r2 



(No. 5 Supplement to Machinery, Sept., 



Specific Gravity of Gases 
Air = I. 

Hydrogen 0.069 

Marsh gas o . 559 

Steam o. 623 

Carbonic oxide o . 968 

Nitrogen o . 971 

defiant gas o . 978 

Oxygen i . 106 

Sulphuretted hydrogen i .191 

Nitrous oxide i . 527 

Carbonic acid i . 529 

Sulphuric acid 2 . 247 

Chlorine 2 . 470 



igS 



Mechanics 



Specific Gravity of Various Substances 

Water = i. 



Substances 



Air at 60° F. under pressure of one atmosphere weighs 

Hi 5 part as much as water at 60° F 

Alcohol 

Ash, American, white, dry 

Aluminum 

Antimony 

Asphaltum 

Basalt 

Bismuth 



Copper and zinc, cast 

Copper and zinc, rolled. . . 

Bronze, copper 8, tin i 

Brick, pressed 

Brick, common, hard 

Brick, soft 

Box wood 

Carbonic acid '. . 

Charcoal, of pines and oaks. 
Chalk 



Clay, dry, in lump, loose 

Coke: 

Loose 

A heaped bushel 35 to 42 pounds. A ton occupies 
from 40 to 43 cubic feet. 

Cherry, dry 

Coal: 

Anthracite , 

Anthracite, broken, loose , 

Bituminous 

Bituminous, broken, loose 

A heaped bushel weighs from 70 to 78 pounds. 
A ton occupies from 43 to 48 cubic feet. 
Cement: 

Rosendale, ground, loose 

Rosendale, struck bushel , 

English Portland 

French Portland 

Copper, cast , 

Copper, rolled , 

Diamond 

Earth: 

Dry loam, loose 

Dry loam, shaken 

Dry loam, moderately rammed 

Loam, moist, loose 

Loam, moist, shaken 

Soft mud : 

Elm, dry 

Ebony 



Average 
specific 
gravity 



0.00123 

0.834 

0.61 

2.6 

6.70 

1-4 

2.9 

9-74 

8.1 
8.4 
8.5 



0.96 
0.00187 



0.672 

i.S 

1-35 



8.7 
8.9 
3. S3 



0.56 
1.22 



Specific Gravity of- Various Substances 199 

Specific Gravity of Various Substances — {Continued) 



Substances 



Fat 

Flint 

Feldspar 

Glass 

Glass, common window. 

Granite 

Gneiss, common 

Gypsum, plaster Paris. . 

Greenstone, trap 

Gravel 



Gold, pure ^ 

Gutta percha 

Hornblende, black 

Hydrogen is 14}^ times lighter than air and 16 times 

lighter than oxygen 

Hemlock, dry 

Hickory, dry 

Iron, cast 

Iron, pure 

Iron, wrought, rolled 

Iron, sheets 

Ivory 



Ice 

India rubber 

Lignum Vitse, dry. 
Lard 



Lead 

Limestones and marbles 

Lime, quick 

Lime, quick, ground loose, per struck bushel. 
Mahogany: 

Dry, San Domingo 

Dry, Honduras 

Maple, dry 

Marbles, see Limestone 
Masonry: 

Granite or limestone 

Granite or limestone rubble 

Brick, ordinary quality 

Mercury at 32° F 

Mercury at 212° F 

Mica 



Mortar, hardened . . 
Mud: 

Dry 

Moist 

Wet, fluid 

Naphtha 

Nitrogen 

Oak live, dry 

Oak white 

Oak, red and black. 



Average 
specific 
gravity 



• 93 
2.6 
2.65 
2.98 
2.52 
2.72 
2.69 
2.27 
30 



19.258 



3-25 



• 4 
.85 

7.218 

7-77 

7.69 

7.73 

1.82 

• 92 
•93 

1-33 

• 95 
11.38 

2.7 
1^5 



13^62 

13.38 

2.93 

1.65 



.848 
.001194 
.95 
• 77 



Average 
weight per 
cubic foot 
in pounds 



58.0 
162.0 
166.0 
186.0 
157^0 
170.0 
168.0 
141. 6 
187.0 
90 to 106 
1204.0 

61. 1 
203.0 

.00527 

25.0 

53.0 
450.0 
485.0 
480.0 
485.0 
114. o 

57.4 
58.0 
83.0 

59.3 
709.6 
168.0 

95.0 

S3 

53 -o 
35 •o 
49 o 



165.0 
154 o 
125.0 
849.0 
836.0 
183.0 
103.0 

80 to no 
no to 130 
104 to 120 

52.9 
.0744 

59-3 

48.0 

32 to 45 



200 



Mechanics 



Specific Gravity of Various Substances — {Continued) 



Substances 


Average 
specific 
gravity 


Average 
weight per 
cubic foot 
in pounds 


Oil: 
Whale 


• 92 
.92 
•94 

• 969 
.860 

• 87 

• 914 
.926 

2.2 

4.129 
4-344 
5 -452 
4.057 
4.789 
4-9 
5-00 
4.029 
5-218 
3-81 
3.863 
7.20 
7.22 
6.45 
3.525 
.00136 


57^3 


Olive 






Palm 










54-3 


Rape seed 


Sunflower 




Oolites 


137 


Ores: 

Copper, vitreous 




Copper, pyrites 




Copper, Cornish 




Iron, chromate 




Iron, pyrites 





































Tin, Cornish 




Zinc, calamine 




Oxygen 


0846 


Peat, dry 


20 to 30 


Pine, white, dry. 


.40 
.55 
-72 

I-15 

1. 176 

1.0 

2.73 
21.5 

2.65 

3.9 

I.I 


25 




34-3 






Pitch 




Plaster Paris 








62.3 




















68.6 


Salt: 

Coarse, Syracuse struck bushel, 56 pounds 

Coarse, Turk's Island struck bushel, 76 to 80 

Coarse, Liverpool struck bushel, 50 to 55 

Sand, dry and loose, average 98 

Sand, wet 


45-0 
62.0 
42.0 

goto 106 
118 to 129 


Sand stones 


2.41 
2.6 


151 


Serpentines . 


162.0 


Snow: 
Freshly fallen 


5 to 12 






IS to so 




.59 
2.6 
2.8 


37-0 




162.0 


Slate 


I7S-0 







Specific Gravity of Various Substances 201 

Specefic Gravity of Various Substances — {Continued) 



Substances 



Silver 

Soapstone (steatite) 

Steel 

Sutphur 

Spruce, dry 

Spelter, zinc 

Tallow 

Tar ; 

Trap 

Topaz 

Tin 

Water: 

Distilled at 32° F. , barometer 30" 

Distilled at 62° F., barometer 30" 

Distilled at 212° F., barometer 30" 

At 60° F. a cubic inch of water weighs .03607 pounds 
or .57712 ounces, avoirdupois 

Sea — 

Dead Sea 

Wax, bees 

Wines 

Walnut, black, dry 

Zinc 

Zircon 

Asbestos 

Acid: 

Acetic 

Carbolic 

Hydrochloric 

Nitric 

Sulphuric 

Barytes 

Brick: 

Common 

Fire 

Clay, fire 

Carbon, graphite 

Manganese 

Magnesium 

Nickel 

Potassium 

Phosphorus 

Silicon 

Stone (building) 

Titanium 

Tungsten 

Uranium 

Vanadium 



Average 
specific 
gravity 



10.5 
2.73 
7.8s 
2.0 

• 4 
7.0 

•94 
i.o 
3.0 
3.55 
7-35 



1.240 

•97 

.998 

.61 

7.0 

4.45 



Average 
weight per 
cubic foot 
in pounds 



655 o 
170.0 
490.0 
125.0 

25.0 
437.5 

58.6 

62.4 
187.0 

459 o 

62.417 
62.355 
59-7 



64.08 

60.5 

62.3 

38.0 

437.5 



.993 

1.063 
1.065 
1.270 
1. 554 
1.970 
4.86 

1.90 
2.2 
2.16 
2.585 
8.01 
2.04 
8.80 
.865 
1.863 
2.493 
2.9 
5.3 

19.26 

18.4 
55 



499 .o 
548.7 



50^ 



Mechanics 
Table of Physical Constants 



Name 



Aluminum . . . 
Antimony — 

Arsenic 

Bismuth 

Calcium 

Carbon 

Chlorine 

Chromium.. . 

Copper 

Gold 

Hydrogen 

Iodine '. . . 

Iron 

Lead 

Magnesium. . . 
Manganese . . . 

Mercury 

Molybdenum. 

Nickel 

Nitrogen 

Oxygen 

Phosphorus . . 

Platinum 

Potassium — 

Silicon 

Silver 

Sodium 

Sulphur 

Tellurium 

Titanium 

Tin 

Tungsten 

Uranium 

Vanadium . . . 
Zinc 



Sym- 
bol 



Al 

Sb 

As 

Bi 

Ca 

C 

CI 

Cr 

Cu 

Au 

H 

I 

Fe 

Pb 

Mg 

Mn 

Hg 

Mo 

Ni 

N 

O 

P 

Pt 

K 

Si 

Ag 

Na 

S 

Te 

Ti 

Sn 

W 

u 

V 
Zn 



Atomic 
weight 



27.3 

122.0 
74-9 

207. 5 
39-9 
11-97 
35.36 
52.4 
63.3 

196.2 
i.o 

126.53 
55-9 

206.4 
23.94 
54.8 

199.8 
95.8 
58.6 
14.01 
15.96 
30.94 

196.7 
39.04 
28.0 

107.66 
23.0 
31.98 



117. 8 
184.0 
180.0 
51.2 
64.9- 



Specific 

heat, 

water 

= I 



.214 

.0508 

.0814 

.0308 

.170 

.214 



.0952 
.0324 
3.2963 
.0541 
.114* 
.0314 
.25 
.122 
•0317 
.0722 
.109 
.244 
.218 
.190 
.0324 
.166 
.2029 
.0570 
.293 
.203 
.0474 

.0562 
.0334 



.0955 



Specific 

gravity, 

water 

= I 



2.6 
6.7 
5. 95 
9.74 
1.578 
2.35 
2.43 
6.8 
8.90 
19.258 

4.94 
7.80 

11.38 
1.70 
8.0 

13.62 
8.64 
8.90 



1.83 

21.53 

.865 

2.49 

10.50 

.972 

2.00 

6.6s 

5.3 

7-35 

17.50 

18.40 

5.54 

7.00 



Specific 
gravity, 

air 

= I 



.069 



.971 
1. 106 



(5. so) 



Melting 
point 



Latent 
heat of 
fusion 



1182° F. 

I973°-Ii34° F. 

774° F. 

497°-484° F. 



>Pt. 
1994° F. 
2ois° F. 

22S° F. 

i9oo°-279o° F. 

6i7°-588° F. 

1139° F. 

2240° F. 

39° F. 

2610° F. 



115° F. 

3150° F. 

I44.5°-I36° F. 

2574° F. 

1732° F. 

207.7°-i9o° F. 

226° F. 

700° F. 

4000° F. 

442°-4i7* F. 

>Mn 

4300° F. 
773°-754° F. 



28.5 
40.0 



43.0 
16.0 



88.69 

II. o 



5.09 
68.0 



9.06 
24.00 
16.0 
128.0 
23.0 
32.0 
16.86 
19.0 

25.65 



48.36 



* Cast iron specific heat at 



212° F. is .109. 
572° F. is .140. 
2x50° F. is .190. 



Table of Physical Constants 
Table of Physical Constants 



203 





Air = I 


Specific heat at 
constant pressure 


Specific 
heat at 
constant 
volume 


Pounds 

per 

cubic 

foot 


Cubic 


Substances 


Specific 
gravity 


For 

equal 

weight, 

water 

= 1 


For 

equal 

volumes 


feet 

per 

pound 


Air 


I 

I . 1056 

.4713 

.0692 

.9670 

1.5210 

.5527 

.9672 

.6220 

.5894 

I. 5241 

1.0384 

I . 1746 

2.2112 

2.4502 

5. 4772 

2.6258 

1.2596 


.2377 
.2175 
.2438 
3.4090 
.2450 
.2169 
.5929 
.4040 
.4805 
.5084 
.2262 
.2317 
.2432 
.1544 
.1210 
.0555 
.1569 
.1882 
.335 
.700 
.450 
.426 


2:^77 


■ 
.1689 
.1550 
.1730 
2.4060 
.1730 
.1710 
.4670 
.3320 


.080728 
.089210 
.078420 
.005610 
.078100 
. 123430 
.044880 
.079490 


12.387 






2405 
2368 
2359 
2370 
3307 
3277 
4106 
2989 
2996 
0447 
2406 
2857 
3414 
2965 
3040 
4122 
2333 


11.209 




12.752 


Hydrogen 

Carbon monoxide 

Carbon dioxide .... 


178.230 
12.804 
8.102 


Marsh gas 

defiant gas (ethylene) . . . 

Aqueous vapor 

Ammonia 

Nitrous monoxide 

Nitrous dioxide 


22.301 
12.580 














Bromine vapor 




Carbon bisulphide vapor . 

Hydrochloric acid 

Sulphuric acid 




Alcohol 



































204 ^ Mechanics 

Weight of Air Required for Combustion of Coal 



Substances 


Pounds of 
air 


B.t.u. from 
combustion 
of one pound 


Carbon 


12.30 
35.00 
18.00 
15.60 


14,500 
61,524 
24,021 
21,524 
18,260 















Boiling Points at Sea Level 

Water 100 ° C. 

Alcohol 78.4 " 

Ether 34.9 " 

Carbon bisulphide 46. i " 

Nitric acid (strong) 120.0 " 

Sulphuric acid 326.6 " 

Oil turpentine 157 . o " 

Mercury : 35o.o " 

Aldehyde 20.8 " 



Combining Equivalents 

Oxygen 

Hydrogen i 

Nitrogen 14 

Carbon 6 

Sulphtir 8 

Phosphorus 10 

Chlorine 35 

Iodine 25 

Potassium 39 

Iron 28 

Copper 31 

Lead 103 

Silver 108 

Bromine 80 

Sodium 23 , 

Fluorine 19. 

Lithium 7 , 

Rubidium 85. 



8.0 "C. 



Lineal Expansion for Solids 



205 



Lesteal Expansion for Solids at Ordinary Temperature 
FOR i°F. 



Solids 



Aluminum, cast 

Antimony, cryst 

Brass, cast 

Brass, plate 

Brick 

Bronze (copper, 17; tin, 2}^; zinc, i). . 

Bismuth 

Cement, Portland (mixed), pure 

Concrete: cement, mortar and pebbles 

Copper 

Ebonite 

Glass, English flint 

Glass, hard 

Glass, thermometer 

Granite (gray, dry) 

Granite (red, dry) 

Gold, pure 

Iron (wrought) 

Iron (cast) 

Lead 

Marbles, various j ^^ 

Masonry, brick w^ 

Merctiry (cubic expansion) 

Nickel 

Pewter 

Plaster, white 

Platinum 

Porcelain 

Silver, pure 

Slate 

Steel, cast 

Steel, tempered 

Stone, sand, dry 

Tin 

Wedgewood (ware) 

Wood, pine 

Zinc 

Zinc 8 ) 

Tin I 



From 1° F. 



Length 

00001234 

00000627 

00000957 

00001052 

00000306 

00000986 

00000975 

00000594 

00000795 

00000887 

00004278 

00000451 

00000397 

00000499 

00000438 

00000498 

00000786 

00000648 

00000556 

00001571 

00000308 

00000786 

00000256 

00000494 

00009984 

00000695 

00001129 

00000922 

00000479 

00000200 

00001079 

00000577 

00000636 

00000689 

00000652 

00001163 

00000489 

00000276 

00001407 

00001496 



Coefficient 

of expansion 

from 32° to 

212° F. 



.002221 
.001129 
.001722 
.001894 
.000550 
.001774 
•OOI75S 
.001070 
.001430 
.001596 
. 007700 
.000812 
.000714 
. 000897 
.000789 
. 000897 
.00141S 
.001166 

. OOIOOI 

.002828 
.000554 
.001415 
.000460 
.000890 
.017971 
.001251 
.002033 
.001660 
.000863 
.000360 
.001943 
.001038 
.001144 
.001240 
.001174 
.002094 
.000881 
.000496 
.002532 
. 002692 



Cubical expansion or expansion of volume equals lineal expansion multiplied by 3. 
The coefficient of expansion from 32° to 212° F. divided by 100 gives the lineal 
expansion for corresponding solid for 1° C. 
The expansion of metals above 212° F. is irregular and more rapid. 



2o6 Mechanics 

Furnace Temperatures 

M. Le Chatelier finds the melting heat of white cast iron 2075° F., 
and that of gray cast iron at 2228° F. Mild steel melts at 2687° F., semi- 
mild at 2651° F. and hard steel at 2570° F. 

The furnace for hard porcelain at the end of the baking has a heat of 
2498° F. The heat of a normal incandescent lamp is 3272° F., but it 
may be pushed beyond 3812° F. 

The following are some of the temperatures determined by Professor 
Roberts-Austin. 

Ten-ton Open-hearth Furnace {Woolwich Arsenal) 
Temperature of steel, 0.3 per cent carbon, pouring into ladle . . . 2993° F. 
Temperature of steel, 0.3 per cent carbon, pouring into large 

mold 2876° F. 

Reheating furnace, Woolwich Arsenal, temperature of interior. . 1 706° F. 
Cupola furnace, temperature of No. 2 cast iron pouring into 

ladle 2912° F. 

Determinations by M. Le Chatelier. Bessemer Process. 
Six-ton Converter 

Bath of slag 2876° F. 

Metal in ladle 2984° F. 

Metal in ingot mold 2876° F. 

Ingot in reheating furnace . . 2192° F. 

Ingot imder the hammer 1976° F. 

Open-hearth Furnace {Siemans) Semi-mild Steel 

Fuel gas near gas generator 1328° F. 

Fuel gas entering into bottom of regenerator chamber . . . 752"° F. 

Fuel gas issuing from regenerator chamber 2192° F. 

Air issuing from regenerator chamber 1832° F. 

Chimney Gases 
Furnace in perfect condition 590° F. 

Open-hearth Furnace 

End of the melting of pig charge 2588° F. 

Completion of conversion 2732° F. 

Fownes Elementary Chemistry gives relative conductivity of metals 

asfoUows: silver 1000 

Copper 736 

Gold 532 

Brass 236 

Tin 14s 

Iron 119 

Steel 116 

Lead 85 

Platinum 84 

German silver 63 

Bismuth 18 



Measurement of Heat 



207 



MEASUREMENT OF HEAT 
Unit of Heat 

The British thermal unit (B.t.u.) is the quantity of heat required to 
raise the temperature of one pound of pure water one degree Fahrenheit 
at 39.1° F. 

The French thermal unit, or calorie, is the quantity of heat required to 
raise the temperature of one kilogram of pure water one degree Centi- 
grade at 4° C, which is equivalent to 39.1° F. The French calorie is 
equal to 3.968 British thermal units; one B.t.u, is equal to .252 calories. 



Mechanical Equivalent of Heat 

This is the number of foot pounds equivalent to one B.t.u. Joule's 
experiments gave the figure 772, which is known as Joule's equivalent. 
Recent experiments give higher figures and the average is now taken 
to be 778. 

Heat of Combustion in Oxygen oe Various Substances 



Substance 



Hydrogen to liquid water at 0° C 

Hydrogen to steam at 100° C 

Carbon (wood charcoal) to carbonic acid (CO2); ordinary 
temperatures 

Carbon graphite to CO2 •. 

Carbon to carbonic oxide, CO 

Carbonic oxide to CO2 per unit of CO ■ 

CO to CO2 per unit of C = 2H X 2403 

Marsh gas, CH4 to water and CO2 

defiant gas, C2H4 and water and CO2 



Heat 


units 


Cent. 


Fahr. 


( 34,462 


62,032 


S 33,808 


60,854 


( 34,342 


61.816 


28,732 


51,717 


( 8.080 


14,544 


< 7,900 


14,220 


( 8,137 


14,647 


7,901 


14,222 


2,473 


4,451 


( 2,403 


4,325 


< 2,431 


4,376 


( 2.38s 


4,293 


5,607 


10,093 


( 13,120 


23,616 


< 13,108 


23,594 


( 13,063 


23,513 


( 11,858 


21,344 


< 11,942 


21,496 


( 11.957 


21,523 



If one pound of carbon is burned to CO2, generating 14,544 B.t.u., and the CO2 
thus formed is immediately reduced to CO in the presence of glowing carbon, by the 
reaction CO2 + C = 2 CO. the result is the same as if the two pounds of C had been 
burned directly to 2 CO. generating 2 X 4451 = 8902 heat units; consequently 
14,544 — 8902 = 5642 heat units have disappeared or become latent and the reduction 
of CO2 to CO is thus a cooling operation. 

Kent, 4S6. 



208 



Heat 



RADIATION OF HEAT 

Relative Radiating and Reflecting Power of Different 

Substances 



Substances 


Radiating 
or absorb- 
ing power 


Reflecting 
power 


Lampblack 


lOO 

loo 
98 
93 to 98 
90 
85 
25 
23 

2^ 

19 , 

17 

24 

15 

II 

7 

14 
7 
3 




Water - 




Writing paper 






7 to 2 




Ice 


15 
75 
77 
77 
81 


Cast iron, bright polished 


Mercury, about 


Wrought iron, polished 


Zinc, polished 


Steel, polished 


83 
76 
85 
89 
93 
86 


Platinum, polished 


Tin 


Brass, cast, dead polish 


Brass, bright polished 


Copper, varnished 


Copper, hammered 


93 
97 


Silver, polished, bright 





Experiments of Dr. A. M. Mayer give the following: The relative 
radiations from a cube of cast iron, having faces rough, as from the 
foundry, planed, drawfiled and polished; and from the same surfaces 
oiled, are as below (Professor Thurston). 



Surface 


Oiled 


Dry 


Rough 


100 
60 

49 
45 




Planed 


32 
20 


Drawfiled 


Polished 


18 









Relative Nonconducting Power of Materials 
Relative Heat-Conducting Power of Metals 



209 



Metals 


Conduc- 
tivity 


Metals 


Conduc- 
tivity 




1000 
981 
84s 
811 
677 
66s 
641 
608 
628 




436 


Gold 


Tin 




Steel 


397 
380 
359 
287 






Mercury 


Cast iron 


Aluminum 


Lead 


Zinc. 


Antimony, cast, horizontal. . . 

Antimony, cast, vertical 

Bismuth 


215 


Zinc, cast, horizontal. 


192 
61 


Zinc, cast, vertical 









Relative Nonconducting Power of Materials 

(Professor Ordway) 



Substance i inch thick. Heat applied 
310° F. 


Pounds of 
water heated 

10° F. per 

hour through 

I square 

foot 


Solid 

matter in 

I square 

foot I inch 

thick, parts 

in 1000 


Air 
included, 
parts in 

1000 




8.1 
9.6 
10.4 
10.3 
9.8 
10.6 
13.9 
35.7 
12.4 
42.6 
13-7 
15.4 
14. 5 
20.6 
30.9 
49 -o 
48.0 
62.1 
13.0 
14.0 
21.0 
21.7 
18.0 
18.7 
16.7 
22.0 
21.0 
27.0 


56 

SO 

20 
185 

56 
244 
119 
S06 

23 
285 

60 
150 

60 
253 
368 

81 



527 


944 
950 
980 
8iS 
944 
7S6 


2. Live geese feathers 


3. Carded cotton wool 


4. Hair felt 


S. Loose lampblack . . 






881 




494 
977 
715 
940 
850 
940 
747 
632 




10. Compressed calcined magnesia 


12. Compressed carbonate of magnesia . . . 

13. Loose fossil meal 


14. Ground chalk 






919 




18. Sand 


471 


19. Best slag wool 


20. Paper 
























24. Loose rice chaff 






25. Paste of fossil meal with hair 






26. Paste of fossil meal with asbestos 






27. Loose bituminous coal ashes 



















2IO Heat 

Professor Ordway states that later experiments niade with still air 
gave results which differ Uttle from cotton wool, hair felt or compressed 
lampblack. Asbestos is one of the poorest conductors. 

Heat-Conducting Power of Covering Materials 

(J. J. Coleman) 

Mineral wool loo Charcoal 140 

Hair felt 117 Sawdust 163 

Cotton wool ■ . 122 Gas works breeze 230 

Sheep's wool 136 Wood and air space 280 

Infusorial earth 136 

Boiling Points at Atmospheric Pressure 

Ether, sulphuric 100° F. Average sea water 213.2° F. 

Carbon bisulphide 118° F. Saturated brine 226° F. 

Ammonia 140° F. Nitric acid 248° F. 

Chloroform 140° F. Oil of turpentine 315° F. 

Bromine 145° F. Phosphorus 554° F. 

Wood-spirit 150° F. Sulphur 570° F. 

Alcohol 173° F. Sulphuric acid 590° F. 

Benzine 176° F. Linseed oil 597° F. 

Water 212° F. Mercury 676° F. 

The boiling points of liquids increase as the pressure increases. 



Table of Equivalent Temperatures 



211 



Table of Equivalent Temperatures, Centigrade to 
Fahrenheit 



Rule to change the values: Fahr. = " C. + 3.2° 









Cent. = (F. - 32°) 


9' 








Degrees 


Degrees 


Degrees 


Degrees 


Degrees 


Cent. 


Fahr. 


Cent! 


Fahr. 


Cent. 


Fahr. 


Cent. 


Fahr. 


Cent. 


Fahr. 


-10 


+14.0 


22 


71.6 


54 


129.2 


86 


186.8 


190 


374 


- 9 


+15. 8 


23 


73.4 


55 


131. 


87 


188.6 


195 


383 


- 8 


+17.6 


24 


75.2 


56 


132.8 


88 


190.4 


200 


392 


- 7 


+19-4 


25 


77.0 


57 


134.6 


89 


192.2 


20s 


401 


- 6 


+21.2 


26 


78.8 


58 


136.4 


90 


194 


210 


410 


- 5 


+23 


27 


80.6 


59 


138.2 


91 


195.8 


215 


419 


- 4 


+24.8 


28 


82.4 


60 


140.0 


92 


197.6 


220 


428 


- 3 


+26.6 


29 


84.2 


61 


141. 8 


53 


199.4 


225 


437 


— 2 


+28.4 


30 


86.0 


62 


143.6 


94 


201.2 


230 


446 


— I 


+30.2 


31 


87.8 


63 


145.4 


95 


203.0 


235 


455 





+32.0 


32 
33 


89.6 
91.4 


64 
65 


147.2 
149.0 


96 
97 


204.8 
206.6 


240 
245 


464 


+ 1 


33.8 


473 


2 


35.6 


34 


93.2 


66 


150.8 


98 


208.4 


250 


482 


3 


37.4 


35 


95. 


67 


152.6 


99 


210.2 


255 


491 


4 


39-2 
41.0 


36 
37 


96.8 
98.6 


68 
69 


154.4 
156.2 


100 


212 


260 
265 


500 










5 


105 


221 


509 


6 


42.8 


38 


100.4 


70 


158.0 


no 


230 


270 


518 


7 


44.6 


39 


102.2 


71 


159-8 


115 


239 


275 


527 


8 


46.4 


40 


104.0 


72 


161. 6 


120 


248 


280 


536 


9 


48.2 


41 


105.8 


73 


163.4 


125 


257 


285 


545 


10 


50.0 


42 


107.6 


74 


165.2 


130 


266 


290 


554 


II 


51.8 


43 


109.4 


75 


167.0 


135 


275 


295 


563 


12 


53.6 


44 


III. 2 


76 


168.8 


140 


284 


300 


572 


13 


55. 4 


45 


113. 


77 


170.6 


145 


293 


305 


581 


14 


57.2 


46 


114. 8 


78 


172.4 


150 


302 


310 


590 


IS 


59. 


47 


116. 6 


79 


174.2 


155 


311 


315 


599 


16 


60.8 


48 


118. 4 


80 


176.0 


160 


320 


320 


608 


17 


62.6 


49 


120.2 


81 


177.8 


165 


329 


325 


617 


18 


64.4 


50 


122.0 


82 


179.6 


170 


338 


330 


626 


19 


66.2 


51 


123.8 


83 


181. 4 


175 


347 


335 


635 


20 


68.0 


52 


125.6 


84 


183.2 


180 


356 


340 


644 


21 


69.8 


53 


127.4 


85 


185.0 


185 


365 


345 


653 



Data Sheet No. 53, The Foundry, November, 1909. 



212 



Heat 



Table of Equivalent Temperatures, Centigrade to 
Fahrenheit — (Continued) 



Degrees 


Degrees 


Degrees 


Degrees 


Degrees 


Cent. 


Fahr. 


Cent. 


Fahr. 


Cent. 


Fahr. 


Cent. 


Fahr. 


Cent. 


Fahr. 


3SO 


662 


510 


9SO 


670 


1238 


830 


1526 


990 


1814 


355 


671 


515 


959 


675 


1247 


835 


I53S 


995 


1823 


360 


680 


520 


968 


680 


1256 


840 


1544 


1000 


1832 


36s 


689 


525 


977 


68s 


126s 


845 


1553 


loos 


1841 


370 


698 


530 


986 


690 


1274 


850 


1562 


lOIO 


1850 


375 


707 


535 


995 


695 


1283 


855 


1571 


lois 


1859 


380 


716 


540 


1004 


700 


1292 


860 


1580 


1020 


1868 


38s 


725 


545 


1013 


705 


1301 


86s 


IS89 


1025 


1877 


390 


734 


550 


1022 


710 


1310 


870 


1598 


1030 


1886 


395 


743 


555 


1031 


715 


1319 


875 


1607 


1035 


189s 


4CX) 


752 


560 


1040 


720 


1328 


880 


1616 


1040 


1904 


405 


761 


565 


1049 


725 


1337 


885 


162s 


104s 


1913 


410 


770 


570 


1058 


730 


1346 


890 


1634 


1050 


1922 


415 


779 


575 


1067 


735 


1355 


895 


1643 


loss 


1931 


420 


788 


580 


1076 


740 


1364 


900 


1652 


1060 


1940 


425 


797 


585 


1085 


745 


1373 


905 


1661 


1065 


1949 


430 


806 


590 


1094 


' 750 


1382 


910 


1670 


1070 


1958 


435 


815 


595 


1103 


755 


1391 


915 


1679 


107s 


1967 


440 


824 


600 


1112 


760 


1400 


920 


1688 


1080 


1976 


445 


833 


60s 


1121 


765 


1409 


92s 


1697 


1085 


1985 


450 


842 


610 


1130 


770 


1418 


930 


1706 


1090 


1994 


455 


851 


615 


1139 


775 


1427 


935 


1715 


109s 


2003 


460 


860 


620 


1 148 


780 


1436 


940 


1724 


1 100 


2012 


46s 


869 


625 


1157 


785 


1445 


945 


1733 


iios 


2021 


470 


878 


630 


1166 


790 


1454 


9SO 


1742 


mo 


2030 


475 


887 


635 


1175 


795 


1463 


955 


1751 


1115 


2039 


480 


896 


640 


1 184 


800 


1472 


960 


1760 


1 120 


2048 


485 


90s 


64s 


1193 


80s 


1481 


96s 


1769 


1125 


20S7 


490 


914 


650 


1202 


810 


1490 


970 


1778- 


1130 


2066 


495 


923 


655 


1211 


815 


1499 


975 


1787 


1 135 


207s 


500 


932 


660 


1220 


820 


1508 


980 


1796 


1 140 


2084 


S05 


941 


665 


1229 


825 


1517 


985 


1805 


1 145 
I150 


2093 
2102 



Data Sheet No. 54. The Foundry, November, 1909. 



Strength of Materials 
Comparison of Thermometer Scales 



213 



Centi- 
grade 


Reaumur 


Fahren- 
heit 


Centi- 
grade 


Reaumur 


Fahren- 
heit 


Centi- 
grade 


Reaumur 


Fahren- 
heit 


-30 


-24.0 


—22.0 


14 


II. 2 


57.2 


58 


46.4 


136.4 


-28 


-22.4 


— 18.4 


16 


12.8 


60.8 


60 


48.0 


140.0 


-26 


-20.8 


-14.8 


18 


14.4 


64.4 


62 


49-6 


143-6 


-24 


-19.2 


-II. 2 


20 


16.0 


68.0 


64 


51.2 


147-2 


—22 


-17.6 


- 7.6 


22 


17.6 


71.6 


66 


52.8 


150.8 


—20 


-16.0 


- 4-0 


24 


19.2 


75-2 


68 


54-4 


154-4 


-18 


-14.4 


- 0.4 


26 


20.8 


78.8 


70 


56.0 


158.0 


-16 


-12.8 


3.2 


28 


22.4 


82.4 


72 


57.6 


161. 6 


-14 


—II. 2 


6.8 


30 


24.0 


86.0 


74 


59-2 


165.2 


— 12 


- 9.6 


10.4 


32 


25.6 


89.6 


76 


60.8 


168.8 


-10 


- 8.0 


14.0 


34 


27.2 


93.2 


78 


62.4 


172.4 


- 8 


- 6.4 


17.6 


36 


28.8 


96.8 


80 


64.0 


176.0 


- 6 


- 4.8 


21.2 


38 


30.4 


100.4 


82 


65.6 


179.6 


- 4 


- 3.2 


24.8 


40 


32.0 


104.0 


84 


67.2 


183.2 


— 2 


- 1.6 


28.4 


42 


33.6 


107.6 


86 


68.8 


186.8 





0.0 


32.0 


44 


35.2 


III. 2 


88 


70.4 


190.4 


2 


1.6 


35.6 


46 


36.8 


114. 8 


90 


72.0 


194.0 


4 


3.2 


39.2 


48 


38.4 


118. 4 


92 


73.6 


197.6 


6 


4.8 


42.8 


SO 


40.0 


122.0 


94 


75-2 


201.2 


8 


6.4 


46.4 


52 


41.6 


125.6 


96 


76.8 


204.8 


10 


8.0 


50.0 


54 


43.2 


129.2 


98 


78.4 


208.4 


12 


9.6 


53.6 


56 


44.8 


132.8 


100 


80.0 


212.0 



No. 21, Supplement to Machinery, June, 1903. 

Strength of Materials 

(From notes on Machine Design, by permission of the author, Prof. Chas. H. 
Benjamin, Cleveland, O.) 





Ultimate strength 


Elastic 
limit, 
tension 


Modu- 
lus of 
rupture, 
trans- 
verse 


Modu- 
lus of 


Kind of metal 


Ten- 
sile 


Com- 
pression 


Shear- 
ing 


elastic- 
ity, 
tension 


Wrought iron, small bars 

Wrought iron, plates. .... 


55 ,000 
50,000 
45,000 
60,000 
90,000 
90,000 
120,000 

18,000 
36,000 
38,000 
18,000 
24,000 
36,000 
85,000 
58,000 
28,000 


38,000 
100,000 

75.000 

125,000 

12,000 

75,000 

100,000 

132,000 

13.000 


45,000 
40,060 
35,000 
50,000 

80,000 

25,000 
42,000 

24,000 

43,000 


28,000 
25,000 
22,500 
32,000 

50,000 
60,000 
Un- 
certain 
16,000 
18,000 

20,000 
14,000 


40,000 
30,000 

36,000 
30,000 


26,000,000 
25,000,000 
25,000,000 
28,000,000 

29,000,000 
40,000,000 

18,000,000 


Wrought iron, large forgings. . 
Steel, 0. H. plate . . . 


Steel, Bessemer 




Cast iron 

Malleable castings 


Steel castings 


30,000,000 
9,000,000 
15,000,000 
10,000,000 


Brass castings . . 


Copper castings 




Bronze, 10 Al, 90 Cu 




14.000,000 
11,000,000 







214 



Strength of Materials 



Material 


Tension 

per square 

inch 


Compres- 
sion per 
square inch 


Shear per 

square 

inch 






103,272 
318,823 
59.246 
97,908 
37.607 
46,494 
81,114 
98,578 
78,049 
81,735 
92,224 

11,000 
17,207 
ii,Soo 
18,000 
13,500 
8,700 
12,800 
18,000 
10,500 
10,250 
19.500 




















Iron wire 


































Bronze wire 






















Woods: 
Ash......; 


6800 


6280 


Beech 


7000 


5223 


Elm 


7700 
5300 
8000 




Hemlock 




Hickory 


1 


2750 
604s 


Maple 


6800 
7000 


7285 


Oak (white) 


! 


4425 




} 




Oak (live) 


6850 

5400 

8500 

5700 

8000 

Tons per 

square foot 

40 

300 

300 

1200 

250 

1000 


8480 


Pine (white) 


11,000 
15,900 
14,500 
12,500 


2450 
5735 
5255 
47SO 






Walnut (black) 


Brick (pressed) 


i 

! 

1 




Granite 
















Limestone 













Properties of Air 215 

Strength of Lime and Cement Mortar 

Tensile Strength, Pounds per Square Inch 
Age 7 days. 

Lime mortar 8 

20 per cent Rosendale 8.5 

20 per cent Roseland 8.5 

30 per cent Rosendale 11 

30 per cent Portland 16 

40 per cent Rosendale 12 

40 per cent Portland 39 

60 per cent Rosendale 13 

60 per cent Portland 58 

80 per cent Rosendale 18.5 

80 per cent Portland 91 

100 per cent Rosendale 23 

100 per cent Portland 120 

Coefficient of Friction 

If two bodies have plane surfaces in contact and the plane of contact 
be inclined so that one body just begins to slide upon the other, the angle 
made by this plane with a horizontal plane is called the angle of repose. 

The coefficient of friction is the ratio of the ultimate friction to the 
pressure perpendicular to the plane of contact, and is equal to the 
tangent of the angle of repose. 

Thus, if R denotes the friction between the surfaces, Q the perpendicu- 
lar pressure and F the coefficient of friction. Then 

F = ^ and R = FQ. 

Centrifugal Force 

In a revolving body the force expended to deflect it from a rectilinear 
to a curved path is called centrifugal force and is equal to the weight of 
the body multiplied by the square of its velocity in feet per second, 
divided by 32.6 times the radius; or, if F equals centrifugal force, W 
equals weight of body, V equals velocity in feet per second and R equals 

the radius, then F = ;r-^ . If N equals the number of revolutions 

32.16 i? 

per minute, the formula is reduced to F = .000341 WN^R. 

Properties of Air 

Air is a mechanical mixture of the gases, oxygen and nitrogen; 21 
parts oxygen and 79 parts nitrogen by volume, or 23 parts oxygen and 
77 parts nittogen by weight. The weight of pure air at 32° F. and 29.9 
barometer, or 14.6963 pounds per square inch; or 21 16.3 pounds per 



2l6 



Air 



square foot is .080728 pounds. The volume of one pound is 12.387 cubic 
feet. 

Air expands 1/491.2 of its volume for every increase of 1° F., and its 
volume varies inversely as the pressure. 

Volume, Density and Pressure of Air at Various Temperatures 

(D. K. Clark.) 





Volume at 


atmospheric 




Pressure at constant 




pressure 


Density, lbs. 


volume 








per cubic foot 
at atmospheric 




Fahr. 












Cubic feet 


Comparative 


pressure 


Pounds per 


Comparative 




in I pound 


volume 




square inch 


pressure 





11.583 


.881 


.086331 


12 . 96 


.881 


32 


12.387 


.943 


.080728 


13.86 


.943 


40 


12.586 


.958 


.079439 


14.08 


• 958 


SO 


12.840 


■ 977 


.077884 


14.36 


.977 


62 


13. 141 


1. 000 


.076097 


14.70 


1. 000 


70 


13.342 


1. 015 


.074950 


14.92 


1. 015 


80 


13.593 


1.034 


.073565 


15.21 


1.034 


90 


13.845 


T.OS4 


.072230 


15.49 


I OS4 


100 


14.096 


1.073 


.070942 


15.77 


1.073 


no 


14.344 


1.092 


.069721 


16. OS 


1.092 


120 


14.592 


I. Ill 


.068500 


16.33 


I. Ill 


130 


14.846 


1. 130 


.067361 


16.61 


1. 130 


140 


15.100 


1. 149 


.066221 


16.89 


1. 149 


150 


15.351 


1. 168 


.065155 


17.19 


1. 168 


160 


15.603 


1. 187 


.064088 


17.50 


1. 187 


170 


15.854 


1.266 


.063089 


17.76 


1.206 


180 


16 . 106 


1.226 


.062090 


18.02 


1.226 


200 


16.606 


1.264 


.060210 


18.58 


1.264 


210 


16.860 


1.283 


.059313 


18.86 


1.283 


212 


16.910 


1.287 


.059135 


18.92 


1.287 



Pressure of the Atmosphere per Square Inch and per 
Square Foot at Various Readings of the Barometer 

Rule. — Barometer in inches X .4908 = pressure per square inch; pressure per 
square inch X 144 = pressure per square foot. 



Barometer, 
inches 


Pressure per 
square inch, 


Pressure per 
square foot. 


Barometer, 
inches 


Presstire per 
square inch, 


Pressure per 
square foot, 


pounds 


pounds 


pounds 


pounds 


28.00 


13.74 


.1978 


29.75 


14.60 


2102 


28.25 


13.86 


1995 


30 


00 


14.72 


2119 


28.50 


13.98 


2013 


30 


25 


14.84 


2136 


28.75 


14. II 


2031 


30 


50 


14.96 


2154 


29.00 


14.23 


2049 


30 


75 


15.09 


2172 


29.25 


14.35 


2066 


31 


00 


15.21 


2190 


29.50 


14.47 


2083 



















Properties of Air 



217 



Barometric Readings Corresponding with Different 
Altitudes (Kent.) 



Altitude, 


Reading of 


Altitude, 


Reading of 


feet 


barometer, 
inches 


feet 


barometer, 
inches 





30.00 


3763.2 


25.98 


68.9 


29.92 


4163.3 


25.59 


416.7 


29.52 


4568.3 


25.19 


767.7 


29.13 


4983.1 


24.80 


1122.1 


28.74 


5403.2 


24.41 


1486.2 


28.35 


5830.2 


24.01 


■ 1850.4 


27.95 


6243.0 


23.62 


2224.5 


27.55 


6702.9 


23.22 


2599.7 


27.16 


7152.4 


22.83 


2962.1 


26.77 


7605.1 


22.44 


3369. S 


26.38 


8071.0 


22.04 



Horse Power Required to Compress One Cubic Foot of 
Free Air per Minute to a Given Pressure (Richards.) 

Air not cooled during compression; also the horse power required, supposing the 
air to be maintained at constant temperature during the compression. 



Gauge 
pressure 


Air not 
cooled 


Air at 

constant 

temperature 


100 


.22183 


.14578 


90 


.20896 


.13954 


80 


.19521 


.13251 


70 


.17989 


.12606 • 


60 


.164 


.11558 


50 


.14607 


.10565 


40 


.12433 


.093667 


30 


.10346 


.079219 


20 


.076808 


.061188 


10 


.044108 


.036944 


S 


.024007 


.020848 



2l8 



Air 



Horse Power Required to Deliver One Cubic Foot of 

Air per Minute at a Given Pressure (Richards.) 

Air not cooled during compression; also the horse power required, supposing the 
air to be maintained at constant temperature during the compression. 



Gauge 


Air not 


Air at 


pressure 


cooled 


constant 
temperature 


lOO 


I. 7317 


i . 13801 


90 


1.4883 


.99387 


80 


1.25779 


.8528 


70 


1.03683 


.72651 


60 


.83344 


.58729 


SO 


.64291 


.465 


40 


.46271 


.34859 


30 


.31456 


.24086 


20 


.181279 


.14441 


10 


.074106 


.06069 


5 


.032172 


.027938 



In computing the above tables an allowance of 10 per cent has been 
made for friction of the compressor. 



Pressure of Water 



219 



Pressure of Water 

Pressure in Pounds per Square Inch for Different 
Heads of Water (Kent.) 

At 62° F. I foot head 0.433 pound per square inch, 0.433 X 144 = 62.352 pounds 
per cubic foot. 



Head, 
feet 





I 


2 


3 


4 


5 


6 


7 


8 


9 







0.433 


0.866 


1.299 


1.732 


2.165 


2.598 


3.031 


3.464 


3.897 


10 


4 330 


4.763 


5.196 


5.629 


6.062 


6.49s 


6.928 


7.361 


7.794 


8.227 


20 


8.660 


9 093 


9.526 


9-959 


10.392 


10.825 


11.258 


II. 691 


12 . 124 


12.557 


30 


12.990 


13.423 


13.856 


14.298 


14.722 


IS.I5S 


IS. 588 


16.021 


16.454 


16.887 


40 


17.320 


17.753 


18.186 


18.619 


19.052 


19.48s 


19.918 


20.351 


20.784 


21.217 


SO 


21.650 


22.083 


22.516 


22.949 


23.382 


23.819 


24 . 248 


24.681 


25.114 


25.547 


60 


25.980 


26.413 


26.846 


27.279 


27.712 


28.145 


28.578 


29.011 


29.444 


29.877 


70 


30.310 


30.743 


31.176 


31.609 


32.042 


32.475 


32.908 


33.341 


33.774 


34.207 


80 


34.640 


35.073 


35 506 


35.939 


36.372 


36.805 


37.238 


37.671 


38.104 


38.537 


90 


38.970 


39.403 


39.836 


40.269 


40.702 


41.135 


41.568 


42.001 


42.436 


42.867 



Head in Feet of Water, Corresponding to Pressures in 
Pounds per Square Inch (Kent.) 

I pound per square inch 2.30947 feet head, i atmosphere 14.71 pounds per square 
inch 33-94 foot head. 



Pres- 
sure 





I 


2 


3 


4 


5 


6 


7 


8 


9 







2.309 


4.619 


6.928 


9.238 


11.547 


13.857 


16.166 


18.476 


20.78s 


10 


23.0947 


25.404 


27.714 


30.023 


32.333 


34.642 


36.952 


39.261 


41.570 


43.880 


20 


46.1894 


48.499 


50.808 


53.118 


55.427 


57.737 


60.046 


62.356 


64.665 


66.975 


30 


.69.2841 


71.594 


73.903 


76.213 


78.522 


80.831 


83.141 


85.450 


87.760 


90.069 


40 


92.3788 


94.688 


96.998 


99.307 


101.62 


103.93 


106.24 


108.5s 


110.85 


113. 16 


SO 


115.4735 


117.78 


120.09 


122.40 


124.71 


126.02 


129.33 


131.64 


133.95 


136 . 26 


60 


138.5682 


140.88 


143.19 


145.50 


147.81 


150.12 


152.42 


154.73 


157.04 


159. 35 


70 


161.6629 


163.97 


166.28 


168.59 


170.90 


173.21 


175.52 


177.83 


180.14 


182.4s 


80 


184.7576 


187.07 


189.38 


191.69 


194.00 


196.31 


198.61 


200.92 


203.23 


205.54 


90 


207.8523 


210.16 


212.47 


214.78 


217.09 


219.40 


221.71 


224.02 


226.33 


228.64 



Electrical and Mechanical Units 



Equivalent Values of Electrical and Mechanical Units 



Units 


Equivalent value in other units 


I kilowatt hour = 


1,000 watt hours. 

1.34 horse-power hours. 
2,654,200 ft. lbs. 
3,600,000 joules. 
3,412 heat units. 
367,000 kilogram metres. 

.23s lb. carbon, oxidized with perfect efficiency. 
3.53 lbs. water evap. from and at 212° F. 
22.75 lbs. of water raised from 62° F., to 212° F. 


I horse-power hour = 


.746 K.W. hours. 
1,980,000 ft. lbs. 
2,545 heat units. 
273,000 kilogram metres. 

.175 lb. carbon oxidized with perfect efficiency. 
2.64 lbs. water evap. from and at 212° F. 
17 lbs. of water raised from 62° F. to 212° F. 


I kilowatt = 


1,000 watts. 

1.34 horse power. 
2,654,200 ft. lbs. per hour. 
44,240 ft. lbs. per minute. 
737-3 ft. lbs. per second. 
3,412 heat units per hour. 
56.9 heat units per minute. 
.948 heat unit per second. 
.2275 lb. carbon oxidized per hour. 
3.53 lbs. water evap. per hour from and at 212" F. 


I horse power = 


746 watts. 
.746 K.W. 
33.000 ft. lbs. per minute. 
550 ft. lbs. per second. 
2,545 heat units per hour, 
42.4 heat units per minute. 
,707 heat unit per second. 
.175 lb. carbon oxidized per hour. 
2.64 lbs. water evap. per hour from and at 212° F. 


I joule = 


I watt second. 
.000000278 K.W. hour. 
.102 k.g.m. 

.0009477 heat units. J^g^Bj^^^^^^Hfl 


1 foot pound = 


1.356 joules. 
.1383 k.g.m. 
.000000377 K.W. hour. 
.001285 heat unit. 
.0000005 H.P. hour. 



Equivalent Values of Electrical and Mechanical Units 221 



Equivalent Values of Electrical and Mechanical 
Units — {Continued) 



Units 


Equivalent Value in Other Units 


I watt = 


I joule per second. 

.00134 H.P. 
3.412 heat units per hour. 

.7373 ft. lb. per second. 

.0035 lb. of water evap. per hour. 
44.24 ft. lbs. per minute. 


I watt per square inch = 


8.19 heat units per sq. ft. per minute. 
6,371 ft. lbs. per sq. ft. per minute. 
.193 H.P. per sq. ft. 


I heat unit = 


1,055 watt seconds. 
778 ft. lbs. 
107.6 kilogram metres. 

.000293 K.W. hour. 

.000393 H.P. hour. 

.00006S8 lb. of carbon oxidized. 

.001036 lb. water evap. from and at 212° F. 



I heat unit per 

square foot per 

minute = 


. 122 watts per square inch. 
.0176 K.W. per sq. ft. 
.0236 H.P. per sq. ft. 


I kilogram metre = 


7.233 ft. lbs. 
.00000365 H.P. hour. 
.00000272 K.W. hour. 
.0093 heat unit. 


I pound carbon 

oxidized with perfect 

efficiency = 


14,544 heat units. 

I . II lbs. of anthracite coal oxidized. 
2.5 lbs. dry wood, oxidized. 
21 cubic ft. illuminating gas. 
4.26 K.W. hours. 
5.71 H.P. hours. 
11,315,000 ft. lbs. 

15 lbs. water evap. from and at 212° F. 


I pound water 
evaporated from 
and at 212° F. = 


.283 K.W. hour. 
.379 H.P. hour. 
965.7 heat units. 
103,900 k.g.m. 
1,019,000 joules. 
751,300 ft. lbs. 

.0664 lb. of carbon oxidized. 



CHAPTER VI 
ALLOYS 

An alloy is a combination by fusion of two or more metals. The com- 
bination may be a chemical one; generally, however, there is an excess 
of one or more of the constituents. 

Metals do not unite indifferently, but have certain affinities; thus 
zinc and lead do not unite, but either will mix with silver in any pro- 
portion. 

Alloys are generally harder, less ductile and have greater tenacity than 
the mean of their components. The melting point of an alloy is as a rule 
below that of any of its components, and it is more easily oxidized. 

The specific gravity of an alloy may be greater, equal to, or less than 
the mean of its components. 

In alloys of copper and tin the maximum tensile and compressive 
strength is afforded by a mixture containing 82.7 per cent copper and 
17.3 per cent tin. The minimum strength is shown by a composition 
of 62.5 per cent copper and 37.5 per cent tin. 



Alloys of Copper and Tin 



Mean composition by analysis 


Tensile 
strength in 
pounds per 
square inch 


Elastic 

limit in 

pounds per 

square inch 


Crushing 
strength in 


Copper 


Tin 


pounds per 
square inch 






12,760 

24,580 

28,540 

29.430 

32,980 

22,010 

5.585 

2,201 

1.455 

3,010 

6.775 

6,390 

6,4So 

4,780 

3.505 


11,000 
10,000 
19,000 
20,000 




97.89 
92.11 
87.15 
80.95 
76.63 
69.84 
65.34 


I 
7 

12 
18 
23 
29 
34 
43 
55 
76 
88 
91 
96 
100 


90 
80 
75 
84 
24 
88 
47 
17 
28 
29 
47 
39 
31 
00 


34.000 
42,000 
53.000 


22,010 
5,585 
2,201 
1,455 
3.010 
6.775 
3.500 
3.SOO 
2,750 


144,000 
147.000 
84.700 


44.52 
23.3s 
11.49 

8.57 
3.72 


35.800 


10,100 
9,800 
9,800 
6,400 













Composition of Alloys in Common Use in Brass Foundries 223 



Alloys of Copper and Zinc 



Mean composition by analysis 


Tensile 
strength in 
pounds per 
square inch 


Elastic limit 
per cent of 
breaking load 
in pounds per 
square inch 


Crushing 
strength in 
pounds per 
squaye inch 


Copper 


Zinc 


Q7.83 


1.88 
16.98 
23.08 
28.54 
33.50 
38.65 
44.44 
50.14 
52.28 
56.22 
66.23 
77.63 
86.67 
94.59 
100.00 


27,240 
32,600 
30,520 
30,510 
37,800 
41,065 
44,280 
30,990 
24,150 , 

9,170 

1.774 

9,000 
12,413 
18,065 

5.400 






82.93 


26.1 
84.6 
29.S 
25.1 
40.1 
44.00 
54.5 
100. 
100. 
100. 
100. 
100. 
100. 
75.0 




76.6s 
71.20 


42,000 


66.27 




60.94 
55.15 
49.66 
47.56 
43.36 


75.000 
78,000 
117,400 
121,000 


32.94 




20.81 
12.12 


52.152 


4-35 







22,000 



Composition of Alloys in Common Use in Brass Foundries 

(American Machinist.) 



Alloys 



Admiralty metal 

Bell metal 

Brass (yellow)... 

Bush metal 

Gun metal 

Steam metal. . . . 

Hard gun metal . 
Muntz metal. . . . 



Phosphor bronze 



T, . j metal... 
^'■^^^"g I solder.. 



Copper, 


Zinc, 


Tin, 


Lead, 


lbs. 


lbs. 


lbs. 


lbs. 


87 


5 


8 




16 




4 




16 


8 




5 


64 


8 


4 


4 


32 


I 


3 




20 


I 


1.5 


I 


16 




2.5 




60 


40 






92 




8.0 




90 




10. 




16 


3 






50 


50 







For parts of engines on naval 
vessels. 

Bells for ships and factories. 

For plumbers, ship and house 
work. 

Bearing bushes for shafting. 

For pumps and hydraulic work. 

Casting subjected to steam pres- 
sure. 

For heavy bearings. 

For bolts and nuts, forged. Valve 
spindles, etc. 

Phos. tin for valves, pumps and 
general work. 

Phos. tin for cog and worm wheels, 
bushes and bearings. 

Flanges for copper pipe. 

Solder for above flanges. 



224 



x\lloys 
Alloys of Copper, Tin and Zinc 



Analysis original mixture 


Tensile 






strength per 






Cu 


Sn 


Zn 


square inch 


90 


5 


5 


23,660 


85 


5 


10 


28,840 


85 


10 


5 


3S,68o 


80 


5 


15 


37,560 


80 


10 


10 


32,830 


75 


5 


20 


34,960 


75 


7-5 


17. 5 


39.300 


75 


10. 


15.0 


34.000 


75 


15.0 


10. 


28,000 


75 


20.0 


50 


27,660 


70 


5.0 


25.0 


32,940 


70 


7.5 


22.5 


32,400 


70 


10. 


20.0 


26,300 


70 


15.0 


15.0 


27,800 


70 


20.0 


lO.O 


12,900 


67.5 


2.5 


30.0 


45,850 


67.5 


5.0 


27.5 


34,460 


67.5 


7.5 


25.0 


30,000 


65.0 


2.5 


32.5 


38,300 


65.0 


5.0 


30.0 


36,000 


65.0 


10. 


25.0 


22,500 


65.0 


15.0 


20.0 


7.231 


65.0 


20.0 


15.0 


2.665 


60.0 


2.5 


37.5 


57,400 


60.0 


5.0 


35.0 


41,160 


60.0 


10. 


30.0 


21,780 


60.0 


15.0 


25.0 


[ 18,020 


58.22 


2.3 


39-48 


66,500 


55.0 


0.5 


44.5 


68,500 


55.0 


5.0 


40.0 


27,000 


55.0 


lo.o 


35.0 


25.460 


50.0 


5.0 


45.0 


23,000 



Above tables from report of U. S. Test Board, Vol. II, 1881. 



Copper-Nickel Alloys 

(German Silver.) 



Constituents 


Copper, 
lbs. 


Nickel, 
lbs. 


Tin, 
lbs. 


Zinc, 
lbs. 


German silver i 


51.6 
50.2 
75.0 


25.8 
14.8 


22.6 

3.1 

25.0 




Nickel silver 


31.9 







Delta Metal 
Useful Alloys of Copper, Tin and Zinc 



225 



Alloys 



U. S. Navy Dept., journal boxes, and guide 

gibs 

Tobin bronze 

Naval brass 

Composition, U.S. Navy 

Gun metal 

I 

Tough brass for engines 

Bronze for rod boxes 

Bronze subject to shock 

Bronze for pump castings 

Red brass : . 

Bronze, steam whistles 

Bearing metal < 

Gold bronze 



Copper, 


Tin, 


Zinc, 


lbs. 


lbs. 


lbs. 


6 


I 


.25 


82.8 


13.8 


3.4 


58.22 


2.3 


29.48 


62.0 


I.O 


37.0 


88.0 


10. 


2.0 


92.5 


50 


2.5 


91.0 


7.0 


2.0 


85.0 


5.0 


10. 


83.0 


2.0 


15.0 


76. 5 


II. 8 


II. 7 


82.0 


16.0 


2.0 


83.0 


15.0 


1.5 


88.0 


10. 


2.0 


87.0 


4.4 


4.3 


81.0 


17.0 




89.0 


8.0 


3.0 


86.0 


14.0 




74-0 


9.5 


9-5 


98.5 


2.1 


5.6 



Other Metals 



.5 lead. 



4.3 lead. 

2.0 antimony. 



7.0 lead. 
2.8 lead. 



Tobin Bronze 



Constituents 


Pig metal, 
per cent 


Copper 

Zinc 


59.00 

38.40 

2.16 

.11 

.31 


Tin 




Lead 





Tensile strength (cast) 66,000 pounds. 



Delta Metal 



Constituents 


Per cent 


Constituents 


Per cent 




. I to 5 
50.0 to 65 
49-9 to 30 




.1 to 5 




Tin 


Zinc 


Zinc 


1.8 to 45 
98.0 to 40 




Copper . . . 







This metal is said to be very strong and tough. 



226 



Alloys 
Aluminum Bronze 



Aluminum, 
per cent 


Copper, 
per cent 


Tensile strength, 

pounds per square 

inch 


II 
lo 

7.5 
5.0 


89 
90 
92.5 
95-0 


89,600 to 100,800 
73,920 to 89.600 
56,000 to 67,200 
33,600 to 40,320 



Analysis of Bearing-Metal Alloys 



Metal 



Camelia metal 

Anti-friction metal 

White metal 

Salgee anti-friction 

Graphite bearing metal 

Antimonial lead 

Cornish bronze 

Delta metal 

Magnolia metal 

American anti-friction metal 

Tobin bronze 

Graney bronze 

Damascus bronze 

Manganese bronze 

Ajax metal 

Anti-friction metal 

Harrington bronze 

Hard lead .' 

Phosphor bronze 

Extra box metal 



Copper 



70.20 
1.60 



77.83 
92.39 
Trace 

59.00 
75.80 
76.41 
90.52 
81.24 



55-73 



97.72 
76.80 



Tin 



4 


25 


98 


13 


9 


91 


14 


38 


9 


60 


2 


37 






2 


16 


9 


20 


10 


60 


9 


58 


10 


98 




97 


10 


92 


8 


00 



Lead 



14-75 

87.92 

i-iS 

67.73 

80.69 

12.40 

5.10 

83.55 

78.44 

.31 

15.06 

12.52 

7.27 
88.32 

94.40 
9.61 
1500 



Zinc 



85.57 



Tn-ce 

.98 

38.44 



42.67 



Anti- 
mony 



12.08 



16.72 
18.83 



16.45 
18.60 



11.93 
6.03 



Iron 



.07 

Trace 

.65 

.II 



68 

Phos. 

• 94 

.20 



Results of Tests for Wear 



Metal 


Composition 


Rate 

of 
Wear 


Copper 


Tin 


Lead 


Phos. 


Arsenic 


Rtnnrlprrl 


79.70 
87.50 


10.00 
12.50 

10.00 
10.00 


9.50 
7.00 


.80 


.80 
.80 


100 




148 


Copper-tin, second experiment, 
tmmp mptal .... 


153 


Copper-tin, third experiment, 

camp mptal 




147 




89.20 
79.20 


142 




IIS 



Belting 



227 



Concerning the preceding table Dr. Dudley remarks: "We began to 
find evidences that wear of bearing metal alloys varied in accordance 
with the following law. That alloy which has the greatest power of dis- 
tortion without rupture will best resist wear." 



Alloys Containing Antimony 

Various analyses of Babbitt metal. 



Metal 



Babbitt metal 

Babbitt metal for light duty 

Babbitt, hard -I 

Britannia < 

White metal 

Parson's metal 

Richard's metal 

Penton's metal 

French Navy 

German Navy 



Tin 



88.9 
45-5 
85.7 
81.0 
22.0 
85.0 
86.0 
70.0 
16.0 
7.5 
85.0 



Copper 



I 

1.8 

4.0 

3.7 

1-5 

i.o 

2.0 

lO.O 

5.0 

2.0 

4-5 
S-o 
7.0 
7-5 



Anti- 
mony 



5 

8.9 

8.0 

7-4 

13.0 

10. 1 

16.0 

62.0 

lo.o 

1.0 

15.0 



Zinc 



2.9 
1.0 
6.0 



27.0 



79 o 
87.5 



Lead 



2.0 
10. s 



Belting * 

Trautwine gives the ultimate strength of good leather belting at 
3000 pounds per square inch. 

Jones and Laughlin give the breaking strength per inch of width, 
Me thick, of good leather belting as follows: 

In the solid leather 675 pounds. 

At the rivet holes of splices 362 pounds. 

At the lacing holes 210 pounds. 

Safe working load 45 pounds per inch of width for single belts, equiva- 
lent to speed for each inch of width of 720 feet per minute per horse power. 
The efficiency of the double belt compared to that of a single belt is as 
10 is to 7. 
Making D = diameter of pulley in inches. 

R = number of revolutions per minute. 

W = width of belt in inches. 

H = horse power that can be transmitted by the belt; 

th&n for single belts, 

„ DX RXW . 
j± = , 

2750 



228 

and for double belts, 



H = 



Belting 



DXRXW 



1925 
For Width of Belt in Inches 



Single belt 


Double belt 


i?X275o 
^~ DXR 


HX 1925 
^~ DXR 


Revolutions per minute 


HX 2750 
DXW 


HX 1925 
DXW 


Diameter of pulley 


H X 2750 
^= WXR 


ffXi925 
WXR 



These formulae are for open belts and pulleys of same diameter. If 
the arc of contact on the smaller pulley is less than 90 degrees, use the 
following constants for those given in above formulae. 



Degrees 
contact 


Single belt 


Double belt 


90 


6080 


4250 


112]^^ 


4730 


3310 


120 


4400 


3080 


135 


3850 


2700 


150 


3410 


2390 


rsiH 


3220 


2250 



Belt Velocity or Circumferential Speed of Pulleys 229 

Belt Velocity or Circumferential Speed of Pulleys 



i 


Revolutions per minute 


II 


50 


60 


70 


80 


90 


100 


no 


120 


130 


140 


150 


160 


170 


Velocity in feet per minute 


6 


78. 5 


94.2 


no 


126 


141 


157 


173 


188 


204 


220 


235 


251 


267 


7 


91.7 


no 


128 


146 


165 


183 


201 


220 


238 


256 


275 


293 


312 


8 


105 


126 


146 


167 


188 


210 


230 


251 


272 


293 


314 


335 


356 


9 


118 


141 


165 


188 


212 


236 


259 


282 


306 


330 


353 


377 


400 


10 


131 


157 


183 


209 


235 


262 


288 


314 


340 


366 


392 


419 


445 


12 


157 


188 


220 


252 


282 


314 


346 


377 


408 


440 


471 


502 


534 


14 


183 


220 


256 


293 


330 


366 


4oi 


440 


476 


513 


550 


586 


623 


16 


209 


251 


293 


335 


377 


419 


460 


502 


544 


586 


628 


670 


713 


18 


230 


282 


330 


377 


424 


471 


518 


565 


612 


659 


707 


754 


801 


20 


262 


314 


366 


419 


471 


524 


576 


628 


681 


733 


785 


838 


890 


22 


288 


345 


403 


460 


518 


576 


634 


691 


749 


806 


864 


921 


979 


24 


314 


377 


440 


502 


565 


628 


691 


754 


817 


880 


942 


1005 


1068 


26 


340 


408 


476 


545 


622 


681 


749 


817 


885 


953 


1021 


1089 


1157 


28 


380 


440 


513 


586 


659 


733 


806 


880 


^ 953 


1026 


1 100 


1 173 


1246 


30 


393 


471 


550 


628 


706 


785 


864 


942 


1022 


1 100 


1 178 


1256 


1335 


32 


419 


502 


586 


670 


754 


838 


921 


1005 


1089 


1173 


1257 


1340 


1424 


34 


445 


534 


623 


712 


801 


890 


979 


1068 


IIS7 


1246 


1335 


1424 


1513 


36 


471 


565 


659 


754 


848 


942 


1037 


1131 


1225 


1319 


1414 


1508 


1602 


40 


523 


628 


733 


837 


942 


1047 


1152 


1256 


1361 


1466 


1571 


1675 


1780 


48 


628 


754 


879 


1005 


1131 


1257 


1382 


1508 


1633 


1759 


188s 


2010 


2136 


54 


707 


848 


989 


1 131 


1272 


1414 


1555 


1696 


1838 


1979 


2120 


2262 


2403 


60 


785 


942 


1099 


1256 


1414 


1571 


1728 


1885 


2042 


2199 


2356 


2513 


2670 


66 


864 


1036 


1209 


1382 


1550 


1728 


1900 


2073 


2246 


2419 


2592 


2764 


2937 


72 


942 


1131 


1319 


1508 


1696 


1885 


2073 


2262 


2450 


2639 


2827 


3016 


3204 


78 


1021 


1225 


1429 


1633 


1838 


2042 


2245 


2450 


2655 


2859 


3063 


3267 


3472 


84 


1099 


I3I9 


1539 


1754 


1978 


2199 


2419 


2639 


2859 


3079 


3298 


3518 


3738 



Contributed by W. J. Phillips, No. 117, extra data sheet, Machinery, October, 1909. 



230 



Belting 



Belt Velocity or Circumferentl\l Speed of Pulleys 
— (Continued) 



a s 










Revolutions per minute 












180 


190 


200 


210 


220 


230 


240 


250 


260 


270 


280 


290 


300 


PL. 


Velocity in feet per minute 


6 


282 


298 


311 


330 


346 


361 


377 


392 


408 


424 


440 


455 


471 


7 


330 


348 


367 


385 


403 


421 


440 


458 


477 


495 


513 


531 


5SO 


8 


377 


398 


419 


440 


461 


481 


503 


523 


545 


565 


586 


607 


628 


9 


424 


447 


471 


495 


518 


542 


565 


588 


613 


630 


660 


683 


707 


lo 


471 


497 


524 


549 


576 


602 


628 


654 


681 


707 


733 


759 


785 


12 


S6o 


597 


628 


659 


691 


722 


754 


78s 


817 


848 


880 


911 


942 


14 


6S9 


696 


733 


769 


806 


843 


880 


916 


953 


989 


1026 


1063 


1 100 


i6 


754 


796 


838 


879 


921 


963 


1005 


1046 


1089 


1131 


1173 


1214 


1257 


i8 


848 


895 


942 


989 


1037 


1084 


I131 


1 178 


1225 


1272 


1319 


1366 


1414 


20 


942 


995 


1047 


1099 


1152 


1204 


1256 


1309 


1361 


1414 


1466 


1518 


1571 


22 


1037 


1094 


1152 


1209 


1267 


1325 


1382 


1440 


1497 


1555 


1612 


1670 


1728 


24 


1 131 


1194 


1257 


1319 


1382 


1445 


1508 


1671 


1633 


1696 


1759 


1822 


188S 


26 


1225 


1293 


1361 


1429 


1497 


1565 


1633 


1701 


1770 


1838 


1906 


1974 


2042 


28 


1319 


1393 


1466 


1539 


1613 


1686 


1759 


1832 


1906 


1979 


2052 


2126 


2199 


30 


1413 


1492 


1571 


1649 


1728 


1806 


188s 


1963 


2042 


2120 


2199 


2277 


2356 


32 


IS08 


1592 


1675 


1759 


1843 


1927 


2010 


2094 


2178 


2252 


2345 


2429 


2513 


34 


1602 


1691 


1780 


1869 


1958 


2047 


2136 


2225 


2314 


2403 


2492 


2581 


2670 


36 


1696 


1791 


1885 


1978 


2073 


2168 


2262 


2326 


2450 


2545 


2639 


2733 


2827 


40 


1885 


1989 


2094 


2199 


2304 


2513 


2618 


2723 


2827 


2932 


3037 


3141 


3246 


48 


2262 


2387 


2513 


2639 


276s 


2890 


3016 


3142 


3267 


3393 


3518 


3644 


3769 


54 


2545 


2686 


2827 


2969 


31 10 


3251 


3393 


3534 


3676 


3817 


3959 


4100 


4240 


60 


2827 


2984 


3141 


3298 


3456 


3613 


3770 


3927 


4084 


4251 


4398 


4555 


4712 


66 


31 10 


3283 


3455 


3628 


3801 


3974 


4147 


4319 


4492 


4665 


4838 


5010 


5183 


72 


3392 


3581 


3770 


3958 


4147 


4335 


4524 


4713 


4900 


5059 


5278 


5466 


5654 


78 


3676 


3880 


4084 


4288 


4492 


4696 


4900 


5059 


5309 


5513 


5717 


5921 


6125 


84 


3958 


4178 


4398 


4618 


4838 


5058 


5277 


5497 


5717 


5937 


6157 


6377 


6597 



Contributed by W. J. Phillips, No. 117, extra data sheet, Machinery, October, 1909. 



Rules for Calculating Speeds and Diameters of Pulleys 231 

Rules for Calculating Speeds and Diameters of Pulleys 

Proposed speed of grinding spindle being given, to find proper speed 
of countershaft. 

Rule. — Multiply the number of revolutions per minute of the grinding 
spindle by the diameter of its pulley and divide the product by the 
diameter of the driving pulley on the countershaft. 

Speed of countershaft given, to find diameter of pulley to drive grind- 
ing spindle. 

Rule. — Multiply the number of revolutions per minute of the grinding 
spindle by the diameter of its pulley and divide the product by the number 
of revolutions per minute of the countershaft. 

Proposed speed of countershaft given, to find the diameter of pulley 
for the lineshaft. 

Rule. — Multiply the number of revolutions per minute of the counter- 
shaft by the diameter of the tight and loose pulleys and divide the 
product by the number of revolutions per minute of the lineshaft. 

Table of Grinding Wheel Speeds 





Revolutions 


Revolutions 


Revolutions 


Diameter 


pef minute 


per minute 


per minute 


of wheel. 


for surface 


for surface 


for surface 


inches 


speed of 


speed of 


speed of 




4000 feet 


Sooo feet 


6000 feet 


I 


IS>279 


19,099 


22,918 


2 


7,639 


9,549 


11,459 


3 


5,093 


6,366 


7,639 


4 


3,820 


4,775 


5,730 


5 


3,056 


3,820 


4,584 


6 


2,546 


3,183 


3,820 


7 


2,183 


2,728 


3,274 


8 


1,910 


2,387 


2,865 


10 


1,528 


1,910 


2,292 


12 


1,273 


1,592 


1,910 


14 


1,091 


1,364 


1,637 


16 


955 


1,194 


1,432 


18 


849 


1,061 


1,273 


20 


764 


955 


1,146 


22 


694 


868 


1,042 


24 


637 


796 


955 


30 


509 


637 


764 


36 


424 


531 


637 



The revolutions per minute at which wheels are run is dependent on 
conditions and style of machine and the work to be ground. 
Data Sheet, No. 52, The Foundry, October, 1909, 



232 



Flanged Fittings 



Rules for Obtaining Surface Speeds, etc. 

To find surface speed in feet per minute, of a wheel. 

Rule. — Multiply the circumference in feet by its revolutions per 
minute. 

Surface speed and diameter of wheel being given, to find number of 
revolutions of wheel spindle. 

Rule. — Multiply surface speed in feet per minute by 12, and divide 
the product by 3.14 times the diameter of wheel in inches. 



Formulae for Dimensions of Cast Iron, Flanged Fittings 

To withstand Hydraulic Pressures of 30, 100 and 200 Pouitds per 
Square Inch 






|-i--Hii<--A-->; 






I t±.l.Alz 
H-E-4 




Fig. 70. 



Diameter of opening A 

r^,, . , r ' ' 7, ^ (pressure in lbs. per sq. inch) , 

Thickness of pipe B= — ^^^ -^ -f 13.25 in. 

3000 

Thickness of flange C= - — Radius of fillet Z) = -approximately. 

Center to face of flange, 

tee and cross : .E= — |- 2 C, or next half-inch. 

2 

Center to face of flange; 

bends, up to 90° F and G = tang, f -^')[ - ) + 2 C, or next 

half inch. 
Center to face of flange, 

45° Y H = tang. 67^/^° X (-] + 2 C, 

Face to face of flange, 

45° Y 7 = tang. 22H° X ij) 

half inch. 

Diameter of flange /= standard. Number and size of bolts.. . 

K = standard. 



or next half -inch. 



-\- 2 C -\- H, or next 



Formulas for Dimensions of Cast Iron, Flanged Fittings 233 

Diameter of bolt circle . . . Z, = standard. 
Radius on center line of 

bends, up to 90° M and N = ^ r-^* Use first quar- 

(tang.-2S-) 

ter inch below. 

Note. — / and L are alike for 50 and 100 lbs., as both are computed for 100 lbs. Con- 
tributed. No. 43, Data Sheet, Machinery, April, 1905. 



CHAPTER VII 
USEFUL INFORMATION 

Shrinkage or Castings per Foot 

(By F. G. Walker.) 



Metals 



Fractions 
of an inch 



Decimals 
of an inch 



Ptire aluminum , 

Nickel aluminum casting alloy 

" Special Casting Alloy," made by the Pittsburg Reduc- 
tion Co 

Iron, small cylinders 

Iron, pipes 

Iron, girders, beams, etc 

Iron, large cylinders, contraction of diameter at top 

Iron, large cylinders, contraction of diameter at bottom. 

Iron, large cylinders, contraction in length 

Cast iron 

Steel 

Malleable iron , 

Tin 

Britannia 

Thin brass castings 

Thick brass castings 

Zinc 

Lead 

Copper 

Bismuth 



^6 
H6 

Hi 
M 
M 

H2 
1^32 
13/64 
^2 

Me 
Me 

3/16 
5^2 



.2031 
.1875 

.1718 

.0625 

.1250 

.1000 

.6250 

.0830 

.0940 

.1250 

.2500 

.1250 

.0833 

.03125 

.1670 

.1500 

.3125 

.3125 

.1875 

.1563 



Data Sheet, No. 34, The Foundry, January, 1909. 



234 



Rapid Conversion of Gross Tons 



235 



This Table Has Been Arranged for the Rapid Conversion 
OF Gross Tons and Fractions Thereof into Pounds 

Equivalent of gross tons (2240 pounds) in pounds. 



Tons 


Pounds 


Tons 


Pounds 


Tons 


Pounds 


Tons 


Pounds 


15 


33,600 


24 


53,760 


33 


73.920 


42 


94.080 


15^ 


34,160 


24W 


54,320 


33^4 


74.480 


42H 


94,640 


isVii 


34,720 


24!/^ 


54,880 


33i/i 


75.040 


421/^2 


95.200 


15H 


35,280 


24% 


55,440 


333/4 


75,600 


42% 


95.760 


16 


35,840 


25 


56,000 


34 


76,160 


43 


96.320 


mi 


36,400 


25H 


56,560 


mH 


76,720 


431/4 


96.880 


i6i^ 


36,960 


25}^ 


57,120 


Zi>A 


77,280 


431/^ 


97.440 


l63/i 


37,520 


25% 


57,680 


343/4 


77,840 


433/4 


98,000 


17 


38,080 


26 


58,240 


35 


78,400 


44 


98.560 


171/4 


38,640 


261.4 


58,800 


3514 


78,960 


44I/4 


99.120 


17H 


39,200 


261/2 


59.360 


35/2 


79,520 


44 J'^ 


99.680 


17% 


39,760 


263/4 


59.920 


353/4 


80,080 


44% 


100,240 


18 


40,320 


27 


60,480 


36 


80,640 


45 


100,800 


18H 


40,880 


27)'i 


61,040 


361/4 


81,200 


45% 


101,360 


iSi/^ 


41,440 


27H 


61,600 


361/^ 


81,760 


451/^ 


101,920 


183/4 


42,000 


273/4 


62,160 


363/4 


82,320 


453/4 


102,480 


19 


42,560 


28 


62,720 


37 


82,880 


46 


103,040 


19H 


43,120 


281/4 


63,280 


371/4 


83,440 


46% 


103,600 


19H 


43.680 


28K2 


63,840 


37I/2 


84,000 


461-^ 


104,160 


19^4 


44,240 


28% 


64,400 


373/4 


84.560 


46% 


104,720 


20 


44,800 


29 


64,960 


38 


85.120 


47 


105,280 


20H 


45,360 


2914 


65,520 


381/4 


85.680 


47% 


105,840 


20l/i 


45,920 


29!/^ 


66,080 


38/2 


86,240 


47H 


106,400 


20% 


46,480 


29% 


66,640 


383/4 


86,800 


47% 


106,960 


21 


47,040 


30 


67,200 


39 


87,360 


48 


107.520 


21 1/^ 


47,600 


3oJ'4 


67,760 


391/4 


87,920 


481/4 


108,080 


21 1/2 


48,160 


30H 


68,320 


39I/2 


88,480 


481'^ 


108,640 


21% 


48,720 


30% 


68,880 


39% 


89,040 


48% 


109,200 


22 


49,280 


31 


69,440 


40 


89.600 


49 


109,760 


22I/4 


49,840 


31 H 


70,000 


4014 


90,160 


49i/i 


110,320 


22V^ 


50,400 


31V2 


70,560 


40!/^ 


90,720 


49!'^ 


110,880 


22% 
1 


50,960 


313/4 


71,120 


403/4 


91,280 


49^4 


111,440 


23 


51,520 


32 


71,680 


41 


91,840 


50 


112,000 


231/4 


52,080 


321/4 


72,240 


41I/ 


92,400 


So% 


112,560 


23!/^ 


52,640 


32H 


72,800 


41/2 


92,960 


5oi/i 


113.120 


23% 


53,200 


323/4 


73,360 


41% 


93,520 


50% 


113.680 



Data Sheet No. 2, The Foundry, September, 1907. 



236 



Useful Information 



Window Glass 

Table of Number of Panes in a Box 



Size 


Panes 


Size 


Panes 


Size 


Panes 


Size 


Panes 


Size 


Panes 


in 


to a 


m 


to a 


m 


tea 


m 


tea 


m 


to a 


inches 


box 


inches 


box 


inches 


box 


inches 


box 


inches 


box 


8x10 


90 


14X20 


26 


20X42 


9 


26X48 


6 


34X48 


5 


8X12 


75 


14X24 


22 


20X48 


8 


26X60 


5 


34x60 


4 


9X12 


67 


14X36 


14 


22x30 


II 


28X36 


7 


36X40 


5 


9X14 


57 


16X18 


25 


22X36 


9 


28X42 


6 


36X44 


5 


10X12 


60 


16x20 


23 


22X42 


8 


28X56 


5 


36x48 


4 


10X16 


45 


16X24 


19 


22X48 


7 


30X34 


7 


36X54 


4 


12X14 


43 


16X36 


13 


24X30 


10 


30X42 


6 


36X60 


3 


12X18 


34 


18X20 


20 


24X36 


9 


30X48 


5 


40X54 


3 


12X20 


30 


18X24 


17 


24X42 


7 


30X60 


4 


40X72 


3 


12X24 


25 


18x36 


II 


24X48 


6 


32X42 


6 


44X50 


3 


14X16 


32 


20X24 


15 


26X36 


8 


32X48 


5 


44X56 


3 


14X18 


29 


20X30 


12 


26X42 


7 


32X60 


4 







Box Strapping 



~<i^ .-»;^, .-^Nv ■■i!SS^\-v»^- ..v^w^N-iS V-.---^'«fi <>^ 



Fig. 71. 
Improved Trojan Box Strapping 

A soft steel continuous band, without rivets, which allows the nail to 
be driven anywhere. The surface is studded or embossed, as illustrated, 
which not only protects the head of the nail, but stiffens and strengthens 
the strap. Edges are perfectly smooth. Put up in reels of 300 feet. 

Width ■ Yi 5^i Yi I in. 

Per reel $1.00 1.25 1.50 2.00 



Fire Brick and Fire Clay 

An ordinary fire brick measures 9 by 4H by 2}i inches, contains 
101.25 cubic inches and weighs 7 pounds. Specific gravity, 1.93. From 
650 to 700 pounds of fire clay are required to lay 1000 bricks. The 
clay should be used as a thin paste and the joints made as thin as 
possible. 



Fire Clays 237 

Analysis of Fire Clays 

New Jersey Clays: Per cent 

Silica 56 . 80 

Alumina 30 . 08 

Peroxide of iron i . 12 

Titanic acid i . 15 

Potash o. 80 

Water and organic matter 10.50 

100.45 

Pennsylvania Clays: 

Silica 44-395 

Alumina 33-558 

Lime trace 

Peroxide of iron i . 080 

Magnesia o. 108 

Alkalies o . 247 

Titanic acid i . 530 

Water and organic matter 14-575 

95-493 

Stourbridge Clays: 

Silica 40 . 00 

Alumina 37 . 00 

Magnesia 2 . 00 

Potash 9 . 00 

Water 12 . 00 

100.00 

Stourbridge Clays: 

Silica 70 . 00 

Alumina 26 . 60 

Oxide of iron 2 . 00 

Lime i . 00 

Magnesia trace 

100.00 

Fire brick should have a light buff color and when broken present an 
uniform shade throughout the fracture. Bricks weighing over 7 to 7.5 
pounds each contain too large a percentage of iron. 



Useful Information 

Velocity of light is 185,844 miles per second. 

Velocity of soimd at 60° F. is 11 20 feet per second. 

The semiaxis of the earth at the poles is 3949.555 miles. 

The terrestrial radius at 45° latitude is equal to 3936.245 miles. 

Radius of a sphere equal to that of the earth is 3958.412 miles. 

Quadrant of the equator is equal to 6224.413 miles. 



238 



Useful Information 



Quadrant of the meridian 6214.413 miles. 

One degree of the terrestrial meridian is 69.049 miles. 

One degree of longitude on the equator equals 69.164 miles. 

A degree of longitude upon parallel 45 equals 48.988 miles. 

A nautical mile equals 1.153 statute miles and is equal to one minute 
of longitude upon the equator. 

Length of a pendulum beating seconds in vacuum at sea level at New 
York is 39.1012 inches. 

Length of a pendulum beating seconds in vacuum at the equator is 
39.01817 inches. 

Mean distance of the earth from the sun is 95,364,768 miles. 

Time occupied in transmission of light from the sun to the earth is 
8 minutes, 13.2 seconds. 

Force Required to Pull Nails from Various Woods 



Kind of wood 



White pine . 



Yellow pine. 



White oak. 



Chestnut . 



Laiirel. 



Size of 
nail 



8d 

9d 

20 d 

50 d 



6od 

8d 
10 d 
50 d 
60 d 

8d 
20 d 
60 d 

50 d 
6od 

9d 
20 d 



Holding-power per square inch 
of surface in wood, pounds 



Wire naU Cut nail 



167 



318 



651 



450 
455 
477 
347 
363 
340 

695 
755 
596 
604 

1340 
1292 
1018 

664 

702 

1179 
1221 



Mean 



405 



662 



1216 



683 



Trautwine gives the holding power of 6 d nail driven one inch into oak as 507 pounds; 
beech, 667 pounds; elm, 327 pounds; pine (white), 187 pounds; % inch square spike 
driven 4H inches into yellow pine, 2000 pounds; oak, 4000 pounds; locust, 6000 
pounds; H inch square spike in yellow pine, 3000 pounds; Vie square spike six inches 
in yellow pine, 4873 pounds. In all cases the nails or spikes were driven across the 
grain. When driven with the grain the resistance is about one half. 



Weights per Cubic Inch of Metals 



239 



Weights per Cubic Inch of Metals 

Lbs. 

Cast iron o . 263 

Wrought iron o . 281 

Cast steel o . 283 

Copper 0.3225 

Brass o. 3037 

Zinc 0.26 

Lead 0.4103 

Mercury o . 4908 



Temperatures Corresponding to Various Colors 

(Taylor & White.) 



Color 



Dark blood red, black red 

Dark red, blood red, low red 

Dark cherry red 

Medium cherry red , 

Cherry, full red 

Light cherry red, bright cherry red, 

Scaling heat,* light red 

Salmon, orange, free scaling heat . . , 

Light salmon, Ught orange 

Yellow 

Light yellow. 

White 



Temperature, 
degrees F. 



990 
1050 
1 17s 
1250 
I37S 

I5SO 
1650 
1725 
182s 
1975 
2200 



* Heat at which scale forms and adheres, i.e., does not fall away from the piece 
when allowed to cool in air. 



240 



Useful Information 



Iron Ores 

Iron is usually found as an ore in one of the following classifications, 
oxides, carbonates and sulphides. 

The following table gives the subdivisions of these classes and an idea 
of the general composition and character of the different varieties. 



. 


Oxides 


Carbonates 


Sulphides 


Component 
parts 


Anhy- 
drous: 
Red 
hematite 


Hy- 
drated: 
Brown 

hematite 


Magnetic 


Spathic 

0-50 
20-60 

1-25 

O-IO 

0- 5 

0-25 

0- 5 
35-40 
Usually 
absent 

0- 5 


Clay 
iron 
stone 


Pyrites 






50-90 

Usually 

absent 

0- 2 

0- 2 

I-IO 

0- 5 
1-30 
0- 5 
0- 3 

0- I 
5-20 

Includes: 
bog iron 
ore, lake 
ore and 
limonite 


30-70 
15-55 

0- I 
0- 2 

O-IO 

0- 5 
0-25 
0-5 
0- 2 

0- 2 
0- 5 

Includes: 
frank- 
linite or 
spiegel- 
eisen and 
load 
stone. 


O-IO 

30-45 
0- 2 

I-IO 
I-IO 
I-IO 

2-25 
20-3S 
0- 3 

0- 2 
0- 4 

Black-' 
band 


44.28 


Ferric oxide 

Ferrous oxides 

Manganese oxide . . . 


60-95 
0- 5 

0- 2 
0- I 
0- 5 
0- 3 
1-25 
0- 2 
°- 3 

0- I 
0- 5 








Lime 


1. 18 


Silica 


2.34 


Carbon dioxide 

Phosphoric anhy- 
dride. 
Sulphur 


49.07 


Water 




Copper 


2.7s 


Arsenic 




.38 


Zinc . 




.22 


Lead . 








Includes: 
specular 
micace- 
ous and 
kidney 
ores. 





CHAPTER VIII 
IRON 

Physical Properties 

Atomic weight 55.9 

Specific gravity 7 . 80 

Specific heat , o.ii 

Melting point 2600° F. 

Coefiicient of linear expansion. 0.0000065 per o" F. 

Thermal conductivity 11. 9 Silver 100 

Electric " 8 . 34 Mercury i 

Latent heat of fusion 88 B.t.u.. 

Pure iron is termed ferrite. 

In the presence of manganese, chromium, etc., hard carbides (double 
carbides) are formed, known as cementite. 

A mixture of ferrite and cementite is called pearlite. 

Pearhte often consists of alternate layers of ferrite and cementite and 
in this condition, from its pecuhar iridescence, is termed pearlite. 

As carbon increases, ferrite is replaced by pearlite. 

Pearhte is not found in hardened steels. 

In steels saturated with carbon, a point fixed by Professor Arnold as 
.89 per cent carbon, the whole structure is represented by pearlite. 

Steels containing less than .89 per cent carbon are known as unsatu- 
rated; those having over .89 per cent carbon as supersaturated. These 
degrees refer distinctly to iron-carbon steels; for the double carbides the 
point of satiuration is slightly lowered. 

Cementite is a hard and brittle compound, but when interspersed with 
ferrite in the form of pearlite, its brittleness is somewhat neutralized by 
the adjacent ferrite. 

A steel containing well laminated pearlite possesses high ductility 
but less tenacity than when found unsegregated. 

Pig Iron 

Pig iron contains from 92 to 96 per cent metallic iron; the remainder 
is mostly composed of sihcon, sulphur, phosphorus and manganese in 
greatly varying amounts. Cobalt, copper, chromium, aluminimi, nickel, 
sodium, titanium and tungsten appear in some brands in minute quan- 
tities. 

241 



242 Iron 

Specific gravity of cast iron is variously given at 7.08, 7.15 and 7.40. 

Atomic weight, 54.5. 

Specific heat from 32° to 212° F., 0.129 Bystrom. 

" " " " at .572° F., 0.1407 " 

" " at 2150° F., 0.190 Oberhoffer. 
Latent heat of fusion, 88 B.t.u.* 
Total heat in melted iron, 450 B.t.u. 
Critical temperature, 1382° F., Stupakoff. 
Coefi&cient of linear expansion for 32° F., 0.000006. 

" " " " at 1400° F., o.ooooioo. 

Weight per cubic foot, 450 pounds. 
Weight per cubic inch, 0.2604 pounds. 
3.84 cubic inches, i pound. 

Grading Pig Iron 

The usual practice of furnaces has been to grade by fracture. 

The grades are designated, Nos. i, 2, 3, 4 or gray forge; mottled and 
white. 

No. I. — Soft; open grain; dark in color. Used for thin, light 
castings. Does not possess much strength; has great softening 
properties; is mixed advantageously with harder grades; carries large 
percentage of scrap. 

No. 2. — Harder, closer, stronger and color somewhat lighter than No. i. 

No. 3. — Harder, closer, stronger and lighter in color than No. 2; 
and incHnes to gray. 

No. 4 {Gray forge). — Hard, strong, fine grained and light gray color. 

Mottled. — Hard, very strong and close grained. Color presents mot- 
tled or imperfectly mingled gray and white colors. 

White. — Hard and brittle, breaks easily imder sledge but has high 
tensile strength; color white. 

No. I iron running in the spout of the cupola displays few sparks. 
In the ladle its smrface is lively and broken, sometimes flowery. 

Nos. 2 and 3 present similar appearances but less marked. 

Hard irons running from the cupola throw out innumerable sparks; 
in the ladle the surface is dull and unbroken; if disturbed the reaction 
is sluggish. 

One cannot safely be guided by the appearance of the fracture of the 

pig; as when melted it may produce a casting of an entirely different 

character than that indicated. 

* Marker and Oberhoffer have found that the specific heat of iron increases in 
about the same ratio up to within the region of the critical point (1382° P.). After 
this it remains practically constant. 



Grading Pig Iron 



243 



This method of grading is entirely unreliable as to chemical constit- 
uents (and physical characteristics) ; the degree of coarseness of fractiure, 
which affects the grade more than any other property, may be due 
entirely to the rate of cooling. 

Two pigs from the same cast may produce two grades; pigs from 
different beds of the same cast may vary as much as i per cent in silicon 
and .05 in sulphur. 

The character of pig iron is often greatly affected by the accidents of 
the furnace. 

Irons produced from the same furnace at different times, from identical 
mixtures, may differ greatly in their constituents, by reason of different 
thermal conditions existing in the furnace at the time the ores were 
melted. 

Grading by fracture is so unreliable that most foundrymen specify the 
characteristics required. 

The following specifications are from Mr. W. G. Scott of the 
J. I. Case Threshing Machine Co., Racine, Wis. 



No. 


Si, 

not less 

than 


s, 

not over 


P, 

not over 


Mn, 
not less 


Total 
carbon 


I 


2.50 
1.95 
1. 35 


.03 
.04 
•OS 


.60 
.70 
.80 


.50 
.70 
90 








3 









Below these figures for silicon, or .005 above for sulphur means re- 
jection. 



Special pig irons 


Silver gray 


Ferro-silicon 


Manganese 
pig 




3.00 to 5.50 

.04 

.00 

.30 

2. so 


7.00 to 12.50 
.04 


Over 2 . so 








.70 





















In calling for charcoal irons, silicon is asked for from .30 to 2.75; 
sulphur not over .025; phosphorus not over .250; manganese not over 
.70; carbon with range of from 2.50 to 4,50. 

Phosphoric pig irons, for small thin castings, siHcon not under 1.50; 
phosphorus not under i.oo; sulphur not over .055; manganese from .30 
to .90; carbon not under 3.00. 



244 



Iron 



Based on a sliding scale for silicon and sulphur and a minimum for carbon. (Mar- 
shall.) 

No. I Foundry Pig Iron 



Silicon with sulphur 


.1.70 


.010 


to 


to 


3.00 


.050 



Carbon content 



Total carbon over 3 . 20 

Graphitic carbon over 2 . 75 

An increase of .10 silicon for every .003 sulphur. 



Silicon with sulphur 



1.70 


.010 


1.80 


.013 


1.90 


.016 


2.00 


.019 


2.10 


.022 


2.20 


.02s 


2.30 


.028 


2.40 


.031 


2.50 


.034 


2.60 


.037 


2.70 


.040 


2.80 


.043 


2.90 


.046 


3.00 


.050 



No. 2 Foundry Pig Iron 



Silicon with sulphur 


1.20 


.cos 


to 


to 


2.20 


.055 



Carbon content 



Total carbon over 3 00 

Graphitic carbon over 2.50 < 

An increase of .10 silicon for every .005 sulphur. 



Silicon with sulphur 



1.20 


.COS 


1.30 


.010 


1.40 


.CIS 


1.50 


.020 


1.60 


.025 


1.70 


.030 


1.80 


.035 


1.90 


.040 


2.00 


.045 


2.10 


.050 


2.20 


.055 



Foundry Pig Iron 
No. 3 FoxjNDRY Pig Iron 



245 



Silicon with sulphur 


.70 


.COS 


to 


to 


1.70 


.055 



Carbon content 


Silicon with sulphur 


Total carbon over 2.75 

Graphitic carbon over 2 .00 ■ 

An increase of . 10 silicon for every .005 sulphur. 


.70 
.80 
.90 
1. 00 
1. 10 
1.20 
1.30 
1.40 
1.50 
1.60 
1.70 


.COS 
.010 
.015 
.020 
.025 
.030 
.035 
.040 
.045 
.050 
.055 



No. 4 Foundry Pig Iron — (Gray Forge) 



Silicon with sulphur 


.50 


.025 


to 


to 


1.50 


.075 



Carbon content 



Total carbon over 2.00 

Graphitic carbon over i . 25 < 

An increase of .10 silicon for every .005 sulphur. 



Silicon with sulphur 



.50 


.025 


.60 


.030 


.70 


.035 


.80 


.040 


.90 


.04s 


1. 00 


.050 


1. 10 


•OSS 


1.20 


.060 


1.30 


.06s 


1.40 


.070 


1.50 


.075 



246 



Iron 



The wide variation in silicon and sulphur which may occur in irons 
graded by fracture is shown in the Transactions of the American Foundry- 
men's Association, Cleveland Convention; wherein appears a statement 
as to the range of those elements, in the same grades of iron, made by 
the same furnace. 

No. I X varies in siHcon from 1.13 to 3.40 per cent. 
" " " sulphur " 0.013 to 0.053 per cent. 

No. 2 X " " sihcon " 0.67 to 3.30 per cent. 

" " " sulphur " o.oi to 0.049 per cent. 

No. 3 Plain " " sihcon " 1.05 to 3.21 per cent. 
" " " sulphur " o.oi to 0.069 per cent 

After long consideration, a committee of the American Foundry men's 
Association, appointed to suggest a uniform system of grading, submitted 
the following report, which was adopted at the Cincinnati Convention, 
May, 1909. 

AMERICAN FOUNDRYMEN'S ASSOCIATION 

Standard Specifications for Foundry Pig Iron 

Adopted by the American Fowndrymen's Association in Convention, 
Cincinnati, May 20, igog. 

It is recommended that foundry pig iron be bought by analysis, and 
that when so bought these standard specifications be used. 



Percentages and Variations 

In order that there may be uniformity in quotations, the following 
percentages and variations shall be used. (These specifications do not 
advise that all five elements be specified in all contracts for pig iron, but 
do recommend that when these elements are specified that the following 
percentages be used.) 



Silicon 


Sulphur 


Total carbon 


(.25 allowed either way) 


(maximum) 


(minimum) 


1. 00 (La) Code. 


0.04 (Sa) Code. 


3.00 (Ca) Code. 


1.50 (Le) . 


cos (Se) 


3.20 (Ce) 


2.00 (Li) 


0.06 (Si) 


3.40 (Ci) 


2.50 (Lo) 


0.07 (So) 


3.60 (Co) 


3.00 (Lu) 


0.08 (Su) 
0.09 (Sy) 
o.ioi (Sh) 


3.80 (Cu) 



Standard Specifications for Foundry Pig Iron 



247 



Manganese 


Phosphorus 


(.20 either way) 


(.150 either way) 


.20 (Ma) Code. 


.20 (Pa) Code. 


.40 (Me) 


.40 (Pe) 


.60 (Mi) 


.60 (Pi) 


.80 (Mo) 


.80 (Po) 


1.00 (Mu) 


1. 00 (Pu) 


1. 25 (My) 


1.25 (Py) 


1.50 (Mh) 


1.50 (Ph) 



Percentages of any element specified half way between the above shall 
be designated by addition of letter "X" to next lower symbol. 

In case of phosphorus and manganese, the percentages may be used 
as maximum or minimum figures, but unless so specified they will be 
considered to include the variation above given. 

Sampling and Analysis 

Each car load, or its equivalent, shall be considered as a unit in 
sampling. 

One pig of machine-cast, or one-half pig of sand-cast iron shall be taken 
to every four tons in the car, and shall be so chosen from different parts 
of the car, as to represent as nearly as possible the average quality of the 
iron. 

An equal weight of the drilHngs from each pig shall be thoroughly mixed 
to make up the sample for analysis. 

In case of dispute, the sample and analysis shall be made by an inde- 
pendent chemist, mutually agreed upon, if practicable, at the time the 
contract is made. 

It is recomniended that the standard methods of the American 
Foundrymen's Association be used for analysis. Gravimetric methods 
shall be used for sulphur analysis, unless otherwise specified in the 
contract. 

The cost of the resampling and reanalysis shall be borne by the party 



Base or Quoting Price 

The accompanying table may be filled out and may become a part of 
the contract: "B," or base, represents the price agreed upon for a pig 
iron running 2.00 in silicon (with allowed variation 0.25 either way), and 
under 0.05 sulphur. "C" is a constant differential to be determined 
upon at the time the contract is made. 



248 



Iron 



Silicon percentages allow .25 variation either way. Sulphur percentages are maxi- 


mum. 












Silicon 


3-25 


3.00 


2.75 


2.50 


2.25 


Sulphtir — .04 


B + 6C 


B + sC 


B + 4C 


B + 3C 


B+2C 


Sulphur — .05 


B+sC 


B + 4C 


B+3C 


B + 2C 


B + C 


Sulphur — .06 


B + 4C 


B + 3C 


B + 2C 


B + C 


B 


Sulphur — .07 


B+3C 


B + 2C 


B + C 


B 


B-C 


Sulphur — .08 ■. . 


B + 2C 


B + C 


B 


B-C 


B-2C 


Sulphtu- — .09 


B + C 


B 


B-C 


B-2C 


B-3C 


Sulphur — .10 


B 


B-C 


B-2C 


B-3C 


B-4C 


Silicon 


2.00 


1-75 


1.50 


1.25 


1. 00 


Sulphur — .04 


B + C 


B 


B-C 


B-2C 


B-3C 


Sulphur — .OS 


Base 


B-C 


B-2C 


B-3C 


B-4C 


Sulphur — .06 


B-C 


B-2C 


B-3C 


B-4C 


B-sC 


Sulphur— .07 


B-2C 


B-3C 


B-4C 


B-sC 


B-6C 


Sulphur - .08 


B-3C 


B-4C 


B-sC 


B-6C 


B-7C 


Sulphur — .09 


B-4C 


B-sC 


B-6C 


B-7C 


B-8C 


Sulphur— .10 


B-sC 


B-6C 

• 


B-7C 


B-SC 


B-9C 



(This table is for settling any differences which may arise in filling a 
contract, as explained under Penalties and Allowances, and may be used 
to regulate the price of a grade of pig iron which the purchaser desires, 
and the seller agrees to substitute for the one originally specified.) 

Penalties 

In case the iron, when delivered, does not conform to the specifications, 
the buyer shall have the option of either refusing the iron, or accepting 
it on the basis as shown in the table, which must be filled out at the time 
the contract is made. 

Allowances 

In case the furnace cannot for any good reason deliver the iron as 
specified, the purchaser may at his option accept any other analysis 
which the furnace can deliver. The price to be determined by the Base 
Table herewith, which must be filled in at the time the contract is made. 



Machine- Cast Pig Iron 

Pig iron is usually cast in sand beds. The casting machine has of late 
years been adopted by some furnaces and the statement is made that 
machine-cast pig, aside from the freedom from sand, possesses other 
important advantages. That it is more uniform in character; affords 



Machine-Cast Pig Iron 



249 



greater certainty as to its chemical composition; is cleaner and melts 
more readily. 

Machine-cast pig presents a closer grain and is harder than iron cast 
in sand, by reason of the greater percentage of combined carbon. 

Upon remelting, this difference disappears and the castings show the 
same analysis. 

Mr. A. L. Colby, chemist of the Bethlehem Iron Co., gives the follow- 
ing statement regarding an experiment, made to determine the influence 
of the mould upon pig iron. 

"One half of a cast was poured into sand moulds and the other half 
into iron. Equal quantities of drillings from six pigs, selected from 
different parts of that portion of the cast which had been cast in sand 
were taken; and similar drillings were obtained from that portion of the 
cast which had been taken to the casting machine; and each was care- 
fully analyzed, with the following results: 



Cast No. 7602 



Silicon 

Manganese 

Phosphorus 

Sulphur 

Total carbon ' 

Combined carbon 

Graphitic carbon 

Tensile strength per square inch 




"The high tensile strength of the machine-cast iron is due almost 
entirely to the higher percentage of its combined carbon. Some of the 
sand-cast portion of this cast, and some of the machine-cast portion were 
melted separately in the same cupola, keeping all smelting conditions 
as nearly uniform as possible; and castings from each melt were made, 
which were proved by analysis, tensile strength, ability to machine and 
appearance of fracture to be as nearly alike as different things, made 
from the same iron, ever are." 

Regarding this experiment, Mr. W. J. Keep in a communication to 
"The Foundry," remarks: 

"The experiment shows that a pig iron cast in iron moulds with a very 
close grain and high combined carbon and the same iron cast in a sand 
pig mould with open grain and low combined carbon, will each, when 
remelted in a cupola, make castings exactly alike." 



2 so 



Iron 



The following report on the test ingots, cast with the experimental 
castings, supports this statement. 



Constituents 


Sand-cast pig iron ingot 

3H inches square and 

iH feet long 


Machine-cast pig iron 

ingot 3]^ inches square 

and i},^ feet long 


Cast 

horizontally, 

per cent. 


Cast 

vertically, 

per cent 


Cast 

horizontally, 

per cent 


Cast 

vertically, 

per cent 


Silicon 


2.93 
.84 • 
.766 
.071 

3.40 
.470 

2.930 

18,000 
G2 Fi 


2.91 
.85 
.769 
.064 

3.390 
.368 

3.022 

16,300 
G2 Ei 


2.96 
.84 
.772 
.077 

3.364 
.336 

3.028 

17,000 
Gi Fi 


2.9s 




.84 




.764 


Sulphur 

Total carbon 

Combined carbon 

Graphitic carbon. 

Tensile strength 


.071 
3.357 

.257 
3.100 
17,000 


Mark on ingot 


Gi Fi 







The coarse open fracture presented by some pig irons, and which under 
the old system might cause them to be graded as No. i, may be due to 
an excessive amount of manganese and the iron will be hard upon re- 
melting. On the other hand, an iron may have a close grain, by reason 
of the graphitic carbon occurring in a finely divided condition and be 
graded low; when, since it is soft, it should have a much higher grading. 

Charcoal Iron 

Charcoal iron is graded according to fracture. The grades are desig- 
nated by numbers and also as soft foundry; low carbon, 2.5 per cent 
total carbon; medium carbon, 3.5 per cent total carbon; and high car- 
bon, 4.5 per cent carbon. Purchases are usually made on specifications. 

Comparatively little charcoal iron is now used, since its valuable 
properties as regards chill and strength may be imparted to coke irons 
by use of the ferrometalloids and scrap steel. 

Grading Scrap Iron 

Machinery scrap should be free from burnt iron, wrought iron, steel, 
plow points, brake shoes, sash weights, sleigh shoes, chilled iron, stove 
plate and fine scrap; should be broken into pieces weighing not over 
400 pounds. 

Approximately, scrap iron varying in thickness from H inch to i inch, 
may be compared with pig iron carrying from 1.5 per cent to 2 per cent 
silicon and .08 per cent sulphur. 



Grading Scrap Iron 251 

From I inch to 3 inches thick, as compared with pig iron carrying from 
I per cent to 1.75 per cent siHcon and .08 per cent sulphur. Above 3 
inches thick, with an open gray fracture, as ranging in sihcon from .75 
to 2 per cent. 

In white scrap, sihcon is usually very low and sulphur very high. 

Burnt iron is worthless except for sash weights and similar castings. 

The successful grading of scrap iron can only be accomplished by 
experience. 



CHAPTER IX 

INFLUENCE OF THE CHEMICAL CONSTITUENTS 
OF CAST IRON 

Carbon 

Combined carbon increases strength, shrinkage, chill and hardness, 
and closes the gram. 

Graphitic carbon reduces strength, shrinkage, chill, hardness, and tends 
to produce an open grain. 

Silicon softens iron by promoting the formation of graphitic carbon. 
It decreases shrinkage and strength; increases fluidity and opens the 
grain. 

Sulphur hardens iron, increases shrinkage and chill; causes it to set 
quickly in the ladle ("lose its hfe"); produces blow holes, shrinkage 
cracks and dirty iron. 

Phosphorus weakens iron, imparts fluidity, decreases shrinkage and 
lowers the melting point. 

Manganese in large percentages hardens cast iron. It increases 
shrinkage and chill, reduces deflection and tends to convert graphitic 
into combined carbon. In small amoimts by reason of its power to 
remove sulphur and occluded gases, its tendency is to produce sound, 
dense castings, without increased hardness or shrinkage. 

To raise the strength of castings, increase manganese and reduce 
silicon ^nd phosphorus. 

To soften iron, increase silicon and phosphorus. 

To reduce shrinkage, increase sihcon and phosphorus and reduce 
sulphur. 

To prevent blow holes, reduce sulphur and increase manganese. 

To prevent kish (excessive amount of free carbon), increase scrap or 
increase manganese. 

[W. G. Scott.] 

Properties of the Usual Constituents of Cast Iron 
Carbon 

Specific gravity (diamond) 3 . 55 

(graphite). 2.35 

Atomic weight 12 . 

252 



Properties of the Usual Constituents of Cast Iron 253 

Specific heat at 212° F 0.198 

" " 1800° F 0.459 

" " 3000° F 0.52s 

Carbon exists in cast iron as combined and graphitic. 
Professor Turner recognizes two different varieties under each of the 
general subdivisions, as follows: 

(Coarse-grained carbon or graphite. 
Fine-grained carbon, called amorphous carbon, 
or temper graphite. 
P , . /• Combined carbon. 

, J "Missing" carbon, which usually occurs in rela- 

[ tively small quantities in cast iron. 

The amount of carbon which may be absorbed by pure iron at high 
temperatiues is stated differently by different authorities. 

Turner places the limit of satiuation at 4.25 per cent, and cites Saniter's 
experiments as follows: 

"At cementation, heat about 1650° F., 2 per cent; by fusion, about 
2550° F., 4.00 per cent." 

Field states that pure iron at maximum temperatures absorbs 6h 
per cent carbon. 

Keep gives the saturation of charcoal iron when cold as 4 per cent and 
that of anthracite or coke irons as 3.50 per cent to 3.75 per cent. 

The saturation point varies according to the temperature. 

As iron cools below the temperature of saturation, carbon separates 
out in the form of graphitic carbon. At just what temperature this 
separation ceases is not definitely known; it is variously stated at 
1300° F., 1650° F., and as high as 1800° F. 

Since the specific heat of carbon is much greater than that of iron, it 
delays the rate of cooling as the temperature falls. 

In a mixture containing 96 per cent of iron and 4 per cent of carbon, 
the heat evolved by the carbon, during the process of cooling, retards 
the rate of cooling one-seventh. 

According to Field, an iron containing 6\i per cent carbon will dis- 
solve no silicon; and one containing 23 per cent of silicon dissolves no 
carbon. 

Iron having 3 per cent silicon contains approximately 0.3 per cent 
combined carbon. 

With 2 per cent silicon the combined carbon is 0.6 per cent and with 
I per cent silicon 0.9 per cent. 

As the carbon separates out in cooling, it changes from combined to 
graphitic, producing a softer, weaker iron and one having less shrinkage. 



254 Influence of the Chemical Constituents of Cast Iron 

The total carbon in cast iron varies from 2 per cent to 4\i per cent, 
averaging about 3.4 per cent. 

With silicon as high as 8 to 10 per cent, the total carbon falls to 2 
per cent. 

Under the same conditions, the higher the total carbon, the softer the 
iron. A very soft iron may contain as little as 1 per cent combined 
carbon with 3.4 to 3.5 per cent graphitic. 

An increase of .25 per cent total carbon produces a marked increase 
in the softness, and a corresponding decrease in strength and shrinkage. 

Combined carbon increases as the grades grow harder. 

Ordinary soft iron contains from .3 to .5 per cent combined carbon. 

Strong irons carry from .45 to .9 per cent. 

The harder grades run from .6 to i per cent. 

The proportion of combined to graphitic carbon is determined: 

First. — By the total carbon present, as the greater the total carbon, 
the greater will be the proportion of graphitic to combined carbon. 

Second. — By the rate of coohng. Rapid cooling increases the com- 
bined and slow cooling increases graphitic carbon. 

Third. — By the temperature of the iron when it begins to cool. 

The higher the temperature at which the iron is poured, the longer will 
be the time elapsed in cooling and the longer the period for conversion 
of combined to graphitic carbon. 

Fourth. — By the amoimt and kind of other elements present. 

Silicon decreases combined and increases graphitic carbon. With 
increased silicon all the combined carbon may be changed to graphitic. 

An increase of i per cent silicon in cast iron, other conditions remain- 
ing the same, will convert from .35 to .47 per cent of combined into 
graphitic carbon; and imder the same circumstances an increase of 
.47 per cent combined carbon will cause a corresponding decrease in 
silicon. 

Sulphur increases combined carbon as also does manganese. 

Phosphorus prolongs the cooling and thereby affords more time for 
the separation of graphitic carbon. 

Loss or Gain of Carbon in Remelting 

An iron may gain or lose carbon in passing through the cupola. 

There is a tendency to loss of carbon in remelting where the carbon and 
silicon are high, with heavy blast and low percentage of fuel. 

On the other hand, where the carbon and silicon are low, with low blast 
and high percentage of fuel, the tendency is to gain in carbon. 

Hard irons melt more readily than soft; the higher the combined 
carbon, the lower the melting point. 



Loss or Gain of Carbon in Remelting 



255 



Hard irons hold their shape in melting. The melted iron runs from 
bottom and sides of the pig freely, leaving smooth surfaces; while 
gray irons become soft and drop away in lumps presenting ragged 
surfaces. 

Hard irons must be melted hotter than gray for pouring as they set 
much more rapidly. 

In running from the spout of the cupola and in the ladle, hard irons 
throw off great quantities of sparks, and the surface of the iron in the 
ladle is dull and inactive when broken; on the other hand, the soft irons 
seldom emit sparks and present a lively surface in the ladle, breaking 
with innumerable checks, the soft Scotch irons showing peculiar flowery 
surfaces. 

The diagram given below taken from the report of Prof. J. J. Porter, 
"shows the range of combined carbon, which sliould result for each 



1 — I — I — \ — \ — \ — I — I — r 

^ Doited Lives are Percenfs expected on Basis 
— ' of Theory. 

Full Lrnes give Percenfs of Combmed Carbon 
obtained In Actual Castings of Thicknesses 
given (Approximated) 

Irons plotted are all under I Percent Pand 
Mn and 0.10 6. and are Cupola Melted. 
o = Total Carbon, x = Comb. Carbon. 



T/7, 



?S^ 



Se-i 



§^^ 



3 55:= 



^/^ 



,£2 



'^c 



':irj^ 




percentage of silicon (the cooling being normal, i.e., the castings being 
neither chilled nor annealed). " The calculations are made on the theory 
that I per cent of silicon precipitates from solution .45 per cent carbon 
as graphitic carbon. 



256 Influence of the Chemical Constituents of Cast Iron 

For specified purposes Prof. Turner gives the following percentages of 
combined carbon. 



Character of iron 


Combined 
carbon 


Extra soft siliceous gray iron 


.08 






Cast iron of maximum tensile strength 


• 47 


Cast iron of maximum transverse strength 


-47 


Cast iron of maximum crushing strength 


Over 1. 00 







Silicon 

Full lines show approximately the relation existing between the 
thickness of section, per cent of silicon and per cent of combined carbon, 
and are plotted from the actual data there given. 

Atomic weight 28.4 

Specific gravity 2 . 49 

Specific heat .20 B.t.u. 

Pig iron takes up its silicon in the furnace, and the amount so absorbed 
depends largely upon the working temperatures. 

Pure iron dissolves about 23 per cent of silicon. By means of the 
electric furnace iron is made to absorb as much as 80 per cent. Those 
irons containing over 20 per cent are called ferrosilicons; where the 
silicon content runs from 5 to 10 per cent they are called high silicon 
irons. 

Iron always loses silicon in passing through the cupola-, and the amount 
lost depends upon three conditions. 

First. — The amount of oxygen coming in contact with the metal in 
melting; oxidation increases with the blast. 

Second. — Upon the composition of the iron as it is charged into the 
cupola, the loss being greater in irons having a high percentage of silicon 
than in those where the silicon content is low. An iron with 4 per cent 
silicon may lose as much as 2 per cent in melting, while with one very low 
in silicon, the loss may be inappreciable. 

The affinity of iron for sihcon decreases as the latter increases, hence 
the amoimt oxidized increases with increased silicon. 

Third. — The loss of silicon varies also with the percentage of carbon 
present, being greater in high than in low carbon irons. 

Silicon lowers the solvent power of cast iron for carbon, thereby 
reducing the amoimt of combined carbon and increasing the graphitic. 

This influence is the more powerful with the lower percentages of 
silicon; the decrease in combined carbon being particularly rapid as 



Silicon 257 

the silicon rises from o to .75 per cent; then as the silicon continues to 
rise, the decrease in combined carbon grows less and less. 

Silicon and carbon each reduce the solubility of iron for the other. 

The influence of silicon is sometimes rendered less apparent by that 
of other variable elements. 

Silicon is not of itself a softener of cast iron, nor does it, per se, lessen 
shrinkage; but it produces a softening effect and reduces shrinkage by 
changing combined into graphitic carbon; the amount used should be 
just suflicient to force from solution the amount of carbon desired in the 
free state for any particular mixture and to furnish the requisite fluidity. 

For every rise of i per cent silicon in cast iron there will be a corre- 
sponding drop of .45 per cent in combined carbon and vice versa. 

Where iron is melted, very hot silicon unites to some extent with 
sulphur, forming a very volatile sub-sulphide of silicon, thereby re- 
ducing the amount of sulphur absorbed by the iron. 

By reason of its specific heat, silicon retards the cooling of iron to a 
certain extent. It can be made to overcome many difficulties in castings, 
and to control the quality and cost of mixtures, where scrap iron is 
largely used. 

An increase of .2 per cent in silicon decreases shrinkage about .01 inch 
per foot. 

Very high percentages of silicon decrease the fusibility of iron. 

When the percentage of silicon in the casting is above 2 per cent, it has 
a weakening influence. 

Ferrosilicon is mixed with iron in the ladle for softening and reducing 
shrinkage. 

Carbide of siHcon is sometimes charged with the iron in the cupola. 

Regarding the use of silicon. Prof. Turner says: "That at one time 
its presence in cast iron, in all proportions, was regarded as injurious; 
that there was no accurate knowledge of its influence prior to 1885, when 
my first paper on 'The Influence of SiHcon on the Properties of Cast 
Iron' was published in the 'Journal of the Chemical Society.'" 

Summary of Prof. Turner's experiments in the use of silicon. 



Characteristics 



Per cent silicon 



Cast iron yielding maximum hardness 

Cast iron yielding maximum crushing strength 

Cast iron yielding maximum density in mass 

Cast iron yielding maximum crushing tensile and transverse 

strength 

Cast iron yielding maximum tensile strength 

Cast iron yielding maximum softness and general working qualities 



.60 

.80 

1. 00 

1.40 
1.80 
2.50 



258 Influence of the Chemical Constituents of Cast Iron 



The subjoined chart and table giving the effect of silicon on the proper- 
ties of cast iron taken from Prof. Turner, show that the influence of 
silicon is of a uniform character as respects crushing, transverse and 
tensile strength. 




£ 3 4 5 b 7 
Silicon, percent. 

Fig. 73. 



60 



60 



40 



20 



\ 










\ 






J^ 


y 


\ 


^^ 


°>^ 


^ 





2 . 4 
^ilicorij percent. 

Fig. 74. 

Chart No. II, showing the hardness of the same series of test bars, 
was determined by the "Sclerometer." 

The hardness decreased continuously with the additions of silicon until 
2,5 per cent was reached, when further additions caused an increase of 
hardness. 

The addition of silicon to iron free from carbon increases the tensile 
strength and hardness. The influence resembles that of combined car- 
bon on iron or steel, but is less energetic. 



Silicon 



259 



Effects of Silicon on the Properties of Cast Iron 



n 

if 


Cylin- 
ders 


1 
1 


If 


Modulus 

of 
elasticity 


1 




1 

r 

6 


Chemical analysis 


go 

Is 


1 


4) 

1 




c 


a 





1 
1 


i 


i-i 

1 




.5 

I.O 

1.4 

2.0 

2.5 
3.0 
4.0 

S.o 
7.5 
10. 


7.560 
7.510 
7.641 
7-555 
7.518 
7.422 
7-258 
7.183 
7.167 
7.128 
6.978 


72 
52 
42 

22 

22 
22 
27 
32 
42 
57 


Lbs. 

22,720 

27,580 

28,490 

31,^40 

35,180 

32,760 

27,390 

25,280 

22,750 

11,950 

10,630 


25,790,000 
28,670,000 
31,180,000 
23,500,00c 
23,560,000 
25,450,000 
21,150,000 
15,640,000 
18,720,000 
14,750,000 
13,930,000 


Lbs. 
168,700 
204,800 
207,300 
183,900 
137,300 
172,900 
128,700 
105,900 
103,400 
111,000 
76,380 


Lbs. 
2702 
3280 
3370 
3498 
3446 
3534 
2850 
2543 
2342 
150S 
1252 


1.98 
2.00 
2.09 
2.21 
2.18 
1.87 
2.23 
2.01 
2.03 

1.86 
1. 81 


.38 

.10 

.24 

.50 

1.62 

1. 19 

1.43 

I. 81 

1.66 
1.48 
1. 12 


1.60 

1.90 

1.85 

1. 71 

.56 

.68 

.80 

.20 

.37 

.38 

.69 


.19 
.45 
.96 
1.37 
1.96 
2.51 
2.96 
3.92 
4.74 
7.33 
9.80 


.32 
.33 
-33 
.30 

.28 
.26 

• 34 
.33 
.30 
.29 
.21 


.14 
.21 
.26 

!6o 
.75 
.70 
.84 
.95 
1.36 
1.95 


.05 
.05 
.04 
.05 
.03 
.05 
.04 
.03 
-05 
.03 
-04 



Bars one foot long, one inch square, loaded in the center. 



Silicon added to hard iron affects the size of the graphite, since the 
freshly precipitated graphite resulting from such addition is smaller than 
that found in ordinary soft foundry irons. Consequently, the metal is 
closer and stronger. 

Prof. Turner favors increasing sihcon in a mixture of cast iron by the 
use of high silicon pig iron, rather than by that of ferrosilicon, as the 
latter differs both in fusibility and density from the iron, rendering the 
product of the mixture uncertain and irregular. "The ideal method is 
for the founder to have a fairly large stock, including several kinds of 
iron, each separate kind being a little too hard or a little too soft for the 
general run of work, but still not very different from what is required. 
By mixing these irons in suitable proportions, it is then easy to obtain 
any composition which may be desired, it being asstmied, of course, that 
the composition of each variety is already known." 

During the period from 1886 to 1888, Mr. Keep made an exhaustive 
study of the influence of silicon on cast iron. The results of his researches 
as summarized in "Cast Iron" are: 

SiUcon added to white iron changes it to gray; added to gray iron, low 
in sihcon, makes the mixture darker. 

It is the influence of silicon, not the percentage, which produces desir- 
able qualities; and that influence is indirect, acting through the carbon 
which the iron contains. 



'260 Influence of the Chemical Constituents of Cast Iron 

The saturation point of iron for carbon is lowered by the addition of 
silicon, as the carbon is expelled in the graphitic form and caught between 
the grains of the iron producing a grayer color. 

If the total carbon is high, or the combined carbon low, the amount 
of silicon required to produce a particular effect will be correspondingly 
low. Similar effects are produced by a small amount of sihcon acting 
through a prolonged period, by reason of slow cooHng of large castings, 
and by a large amount acting through a short period, as in the rapid 
cooling of small castings. By regulating the amount of silicon in the 
mixture the state of carbon as well as the depth of chill can be controlled. 
The diffusion of silicon is very irregular. Mr. Keep found in a number 
of experiments that the average variation in diffusion was from .09 to 
.24 per cent. This average increases and the diffusion is less and less 
complete as the silicon increases, so that any literal determinatives of 
silicon are rendered more or less approximative (as showing the per- 
centage of silicon in a car load of iron) by the unequal diffusion. 

As regards hardness, the addition of 2 to 3H per cent of silicon will 
convert all the combined into graphitic carbon, which it is possible to 
change by the use of that element. 

Silicon in itself hardens cast iron, but the softening effect caused by 
it in producing the change from combined to graphitic carbon, is such as 
to result in decreased hardness, until the amount of silicon added has 
reached from 2 to 3 per cent. Further additions are not advantageous. 
The beneficial influence resulting from the use of silicon in cast iron is not 
confined to decreased hardness. It imparts fluidity and also tends to 
produce clear, smooth surfaces on the castings, by reason of the liberated 
graphite, in part, interposing itself between the sand and the hot iron. 

Sulphur 

Atomic weight 32 . 

Specific gravity 2 . 03 

Specific heat o. 2026 

Melting point 226** F. 

Latent heat of fusion 16.86 B.t.u. 

Weight per cubic foot 125 pounds 

The sulphur in pig iron is taken up in the furnace, from the fuel and 
flux. Its presence is most injurious and causes the foundryman more 
difiSculty than any other element. It makes iron hard and brittle, 
increases shrinkage and chill, causes iron to congeal quickly and by 
preventing the ready escape of gases, makes blow holes and pin holes. 

It increases the combined carbon and reduces silicon. 



Sulphur 



261 



WTien pig iron is remelted, the percentage of sulphur is always in- 
creased, as it takes up from 20 to 40 per cent of the sulphur in the fuel. 
Mr. J. B. Neu found in some experiments that as much as 66 per cent 
of the sulphur in the fuel was absorbed by the iron in melting. 

The sulphur content of the iron at each of three remeltings is given by 
Mr. Percy Longmuir as follows: 





First 
melt 


Second 
melt 


Third 
melt 


Per cent sulphur 


.04 


.10 


.20 



The proportion between the total amount of sulphur present in the 
fuel, to that absorbed by the iron, is dependent on three conditions. 

First. — The quality and quantity of flux used. 

Second. — The temperature of the melted iron. 

Third. — The composition of the fuel and iron. 

In a hot working cupola, the proper quantity of flux will remove much 
of the sulphur. That present in the fuel as a sulphuretted hydrocarbon 
has no appreciable effect upon the percentage retained in the melted iron. 

As sulphur combines with iron at low temperatures, a hot cupola tends 
to increase the amount carried away by the slag. Where the fuel contains 
I per cent or over of sulphur, it may add from .04 per cent to .06 per cent 
to the iron and a casting made from iron having only 2 per cent of sulphur 
may, when the iron is melted with high sulphur coke, show from .06 
to .08 per cent. 

A slow melting cupola with low temperature favors the absorption of 
sulphur. 

An increase of sulphur, the other elements and the rate of cooling 
remaining constant, hardens iron by increasing the combined carbon and 
also causes greater shrinkage, contraction and chill. 

Less change in the percentage of sulphur present is required to harden 
or soften cast iron than in that of any other element. 

Sulphur shortens the time that iron will remain fluid in the ladle, 
"destroys the life of the iron," and if present to a large extent, makes 
the production of sound castings very difficult. The molten iron is 
sluggish and sets quickly, thereby enclosing escaping gases, dross, kish, 
etc., which cause blow holes and dirty castings. 

Where sulphur is present to any considerable extent, the iron must be 
poured very hot. 

Iron will absorb as much as .3 per cent sulphur with increasing fusi- 
bility and decreasing fluidity. 



262 Influence of the Chemical Constituents of Cast Iron 

An increase of .01 per cent of sulphur can neutralize the effect of from 
.08 to .10 per cent silicon. In coke irons, usually, as the silicon decreases 
the sulphur increases. To maintain a uniform degree of hardness in 
castings the increase of silicon corresponding to successive increases of 
.01 per cent sulphur should be about as follows: 

Sulphur, per cent 01 .02 .03 .04 .05 .06 

Silicon, per cent 2 . 00 2.10 2 . 20 2 . 30 2 . 40 2 . 50 

Sulphur may be largely expelled from cast iron by the use of man- 
ganese, passing off in the slag as sulphide of manganese; the greater the 
amount of manganese present, the less sulphur will the iron absorb and, 
it is possible, where the manganese is very high, for the iron to lose 
sulphur in melting. 

From I to 2 per cent manganese, in addition to that carried by the pig 
iron, is sometimes used in the ladle, to effect the removal of sulphur; 
care must be exercised in this respect, however, as manganese in excess 
of that taken up by the sulphur tends to harden the iron. 

When the fuel does not contain more than .08 per cent sulphur and 
the iron has about .5 per cent manganese, the sulphur in ordinary gray 
irons will increase about .025 per cent in melting. 

The injurious effects of sulphur are largely counteracted by the use of 
phosphorus. Other elements remaining constant, an increase of .1 
per cent phosphorus produces about the same results in counteracting 
the effects of sulphur as does an increase of .25 per cent silicon. 

By the use of phosphorus instead of silicon for this purpose, the 
fluidity of the iron is greatly increased; gases, dross, etc., can come to 
the surface and greater freedom from blow holes, shrink holes, etc., 
results. 

Irons with high combined carbon are usually high in sulphur. Long- 
muir gives the following as the result of examinations of the sulphur 
content for different amounts of combined carbon. 



Grade 



Combined carbon 

Sulphur 

Silicon 



I 


2 


3 


4 


5 


Mottled 


.50 


.60 


.80 


1. 10 


1.30 


1.80 


.02 


.02 


.04 


.08 


.10 


• IS 


2. so 


2.30 


1.80 


1.50 


1.20 


.70 



White 



3.00 
.20 
.30 



The sulphur content of pig iron usually runs from .01 to .08 and some- 
times higher. 

Prof. J. J. Porter concludes his remarks on the effects of sulphur upon 
the physical properties of cast iron as follows: "Through the formation 



Phosphorus 263 

in the iron sulphide of eutectic films, it causes brittleness and weak- 
ness, especially to shock. Through its action on the carbon it increases 
hardness and may either increase or decrease strength according as the 
combined carbon is already too low or too high. It has a great tendency 
to cause blow holes, especially near the upper surface of thick castings. 
So marked is this effect in pig iron that high sulphur pig may nearly 
always be spotted by the presence of blow holes in the top surfaces. 

"Sulphur probably has a more detrimental effect on low silicon, or 
chill iron, than on the ordinary foundry grades. All of these effects of 
sulphur are considerably lessened by the presence of sufficient manganese 
to insure its being in the form of MnS, but on the other hand, the segre- 
gation of MnS may cause bad places in the casting, apparently due to 
dirty iron." 

The statements given above are those generally entertained as regards 
the deleterious influence of sulphur. They are not, however, entirely 
confirmed by the investigations of Prof. Turner and Mr. Keep. The 
former remarks that: "We are still in need of exact information as to the 
influence of sulphur in cast iron." After a long series of experiments to 
determine the injurious effect of sulphur on cast iron, Mr. Keep con- 
cludes that the presence of .05 per cent of that element will not exert any 
appreciable deleterious influence, and that what little ill effect results 
is corrected by a slight increase of silicon. Such small percentage of 
sulphur does not seem to influence the depth of chill, nor does there 
appear to exist any relation between the sulphur content and the strength 
of an ordinary casting. 

"While there is no indication that sulphur is in any way beneficial, on 
the other hand, evidence is lacking to show that its influence is ever any- 
thing but injurious; and the suggestion arises from the records, that the 
prevaiUng opinions regarding the deleterious effects of sulphur are partly 
superstitious, due, largely, to laboratory experiments made under con- 
ditions never met with in the foundry." 

Phosphorus 

Atomic weight 31 • 00 

Specific gravity i . 83 

Specific heat o . 189 

Melting point 112° F. 

Latent heat of fusion 9 . 06 B.t.u. 

Weight per cubic inch . 066 

The phosphorus content in pig iron comes mostly from the ore, but 
also in part from the fuel and flux. 



264 Influence of the Chemical Constituents of Cast Iron 

Phosphorus weakens cast iron, lowers its melting point, imparts 
fluidity, tends to soften and decreases shrinkage. 

It has no direct effect on carbon, but since it prolongs the cooling 
of melted iron it gives more time for graphitic carbon to separate 
out. 

Its influence in imparting fluidity is greater than that of any other 
element, hence its presence within moderate limits (i to 1.25 per cent) is 
especially desirable for light, thin castings. 

After it is once taken up by the iron very little of it escapes, but its 
percentage is frequently increased if it exists to any extent in the fuel 
or flux used in melting. 

Phosphorus largely counteracts the influence of sulphur to increase 
combined carbon, shrinkage, contraction and chill. An increase of 
.1 per cent phosphorus in the iron will produce about the same physical 
results in counteracting the effects of sulphur, as an increase of .25 per 
cent sihcon, all other elements remaining constant. 

Where over .7 per cent phosphorus is present in the iron it tends to 
make the latter cold short and unless there is necessity for extreme 
fluidity the phosphorus content should not exceed i per cent. 

By reason of its tendency to increase fusibiUty, it should be kept as low 
as possible in castings required to stand high temperatures. 

In machinery castings containing 1.5 per cent phosphorus, the tools 
are quickly heated and worn. 

Where great strength is required of castings, the phosphorus content 
should not exceed .02 per cent. 

Where blow-holes are formed in castings, by reason of occluded gases, 
phosphide of iron is frequently extruded into them in the shape of 
globular masses or shot. 

Ferrophosphorus may contain from 20 to 25 per cent phosphorus and 
is sometimes used in the ladle where prolonged fluidity is desired. 

Prof. Turner states that the presence of 0.5 phosphorus in cast iron 
produces excellent results and that where fluidity and soundness are 
more important than strength, from i to 1.5 per cent may be permitted; 
it should not be allowed in excess of the higher hmit. According to 
Prof. Porter, the addition of i per cent phosphorus to iron containing 
3.5 per cent carbon and 2 per cent silicon approximately: 

Lowers the temperature at which freezing begins from 2200° to 2150° F., 
or 50° F. 

Lowers the temperature at which freezing ends from 2165° to 1740° F., 
or 425° F. 

Increases the temperature range of solidification from 50° to 375° F. 



Manganese 265 

Manganese 

Atomic weight 55 • 00 

Specific gravity 8.1 

Specific heat .12 

Melting point 2250° F. 

Latent heat of fusion 

Weight per cubic foot ,506. 25 pounds 

Manganese is a white metal, having a brilliant crystalline fracture. 
It has a strong affinity for oxygen and sulphur, but none for iron; alloys 
with iron in all proportions. 

The manganese in pig iron comes from the ores. Foundry irons 
contain from .2 to 2 per cent manganese. 

Manganese pig from 2 to 10 per cent; spiegeleisen from 15 to 40 per 
cent; ferromanganese from 50 to 90 per cent. 

There is always a loss of manganese in remelting. It escapes by 
volatilization; by oxidation, and if sulphur is present, by uniting with 
it to a greater or less extent. The amount of loss depends on the amount 
of blast and percentage of sulphur present in the fuel. 

With I per cent manganese present in the iron the loss of Mn in re- 
melting varies from .2 to .3 per cent. 

A peculiarity of manganese is that it may impart to pig iron, or castings, 
a very open grain, rendering them apparently soft, even though they are 
quite hard. 

It greatly affects the capacity of iron to retain carbon; where only 
.75 per cent Mn is present in the iron the carbon content may be as high 
as 4 per cent. 

It decreases the magnetism of cast iron and when present to the extent 
of 25 per cent the magnetism disappears. 

As the percentage of manganese in iron increases, that of sulphur 
decreases. 

On the other hand, the higher the manganese, the greater the combined 
carbon. 

Manganese hardens cast iron, promotes shrinkage, contraction and 
chill; but by reason of its affinity for sulphur and its removal of this 
element, it may produce effects precisely the opposite of those above 
stated. However, if the amount of manganese is greater than that 
required for the removal of the sulphur present, the excess causes the 
iron to take up more carbon in combination, and hardness results. 

Increasing manganese above .75 per cent, the other elements remaining 
constant, causes greater contraction and chill on accoimt of its hardening 
influence. These effects may be very pronounced in light castings. 



266 Influence of the Chemical Constituents of Cast Iron 

On account of its strong affinity for oxygen it tends greatly to the 
removal of oxides and occluded gases, thereby preventing blow-holes. 

Manganese pig iron is an ordinary iron, carrying somewhat more 
manganese than the ordinary foimdry irons. 

It is used to raise the combined carbon, to add strength to the mixture, 
to prevent blow-holes, to give life to the iron and for the removal of kish. 

Ferromanganese comes to the fomidry in a fine powder. It is used in 
the ladle in the proportion of about i pound to 600 pounds of iron and 
acts as a purifier, driving out sulphur, softening the iron where hardness 
is due to sulphur and reducing the chance of blow-holes. 

When used in this way the iron must be very hot, as with dull iron it 
does little good. It should be thoroughly incorporated with the iron 
by stirring. It must be used with caution, as irons with low silicon and 
carbon and high manganese are hard and shrinky. 

The use of manganese pig iron in the cupola gives better results, and is 
less expensive than that of ferromanganese in the ladles. 

It is claimed for manganese that it makes hard iron soft and soft iron 
hard. 

With respect to the influence of Mn upon chill, Mr. Keep's views are 
at variance with those above given. He states that manganese does not 
increase chill, but under certain conditions may aid in removing it. 

Aluxmnum 

Atomic weight 27.1 

Specific gravity 2 . 65 

Specific heat o. 212 

Melting point 1182*^ F. 

Latent heat of fusion: 28. 5 B.t.u, 

Weight per cubic foot 165 . 6 pounds 

Almninum is a white metal, resembling silver; very soft and malleable; 
has a great affinity for oxygen; alloys with iron to an unlimited extent. 
It does not occur in pig iron. When added to iron in the ladle it 
should be thoroughly mixed by stirring. 

Its influence on cast iron resembles that of sihcon, in producing a 
softening effect by the conversion of combined into graphitic carbon. 

A white iron to which from .5 to .75 per cent of aluminum has been 
added becomes gray. 

Aluminiun decreases shrinkage and chill, and increases fluidity. By 
reason of its ajffinity for oxygen it tends to prevent the formation of 
blow-holes. 

It closes the grain of irons high in graphitic carbon, but may render 
them sluggish and dirty. When used in amounts exceeding 1.5 to 2 



Titanium 267 

per cent it has a weakening influence. Hard irons containing from 1.25 
to 1.4 per cent combined carbon are made stronger by the addition of 
aluminum. The amount of aluminum which may be used varies from 
.25 to 1.25 per cent; its action is somewhat uncertain and its alloys with 
iron are erratic at times, producing results the reverse of those anticipated. 

Nickel 

Atomic weight 58.7 

Specific gravity 8.8 

Specific heat .11 

Melting point 2610° F. 

Latent heat of fusion 

Weight per cubic foot 550 pounds 

Nickel is a white metal having a silvery color; it is highly ductile and 
does not oxidize readily. Alloys with iron in all proportions. When 
used in quantities varying from .5 to 5 per cent, its tendency is to 
harden, render more dense and increase the tensile strength of cast iron. 
In large amounts it is said to have a softening influence. 

Mr. A. McWilliams found that an alloy of white Sweeds iron with 50 
per cent nickel gave a soft fine gray metal, even when cast in sections 
from I to 3 inches thick, in chills. 

Cast iron containing from 25 to 30 per cent nickel resists corrosion. 

Nickel is little used in cast iron, except where great strength is re- 
quired. It imparts most valuable properties to steel. 

Titanium 

Atomic weight 48 . 00 

Specific gravity 5.3 

Specific heat 

Melting point 4000° F. 

Latent heat of fusion 

Weight per cubic foot 330 pounds 

Titanium is found in many brands of foundry and Bessemer irons, 
running in percentages from a trace to i per cent. It increases the 
strength of cast iron to a marked degree. An addition of from .01 to 
.06 per cent titanium has shown in test bars an increase of 40 per cent 
in transverse strength. 

It has a strong affinity for oxygen and nitrogen. 

Ferroalloys are made to contain from 10 to 30 per cent titanium. 

When ferrotitanium is added to iron in the ladle, it unites with the 
oxygen and nitrogen, the resulting oxides and nitrides passing off in the 



268 Influence of the Chemical Constituents of Cast Iron 

slag; none of the titanium remains in the iron, except when used in large 
quantities; its effect then is to harden the iron. 

Formerly titanic irons were carefully avoided and it does not appear 
that ferrotitanium has as yet been used to any great extent by foundry- 



Investigations by Dr. Richard Moldenke and Mr. G. A. Rossi indicate, 
however, that the use of ferrotitanium promises a marked improvement 
as regards strength and the removal of nitrogen and oxygen from cast 
iron. Mr. Rossi found as the result of his experiments that the addition 
of 4 per cent of a lo per cent ferrotitanium to cast iron increased the 
transverse and tensile strength from 25 to 30 per cent. 

Dr. Moldenke gives the following summary of results obtained by him. 



Mixtures 



Gray 



White 



Original iron 

plus .05 T 

" .10 T 

" .05 T. and carb. 
" .10 " " 
" .IS " " 

Average 



Tests 
9 
4 
3 
6 
6 
4 



Lbs. 
2020 
3100 
3030 
3070 
2990 
3190 



Tests 
8 
II 

9 
10 
10 



3070 



Lbs. 
2030 
2400 



2420 
2400 
2520 



2430 



Increase of strength of treated iron over original 52 per cent — 18 per cent. 

From the above simimary it appears that the greatest increase in 
strength was found in gray iron. 

With vanadium and cast iron the Doctor found results directly con- 
trary to the above. He calls attention to the fact that the improve- 
ment in strength is almost as marked with .05 per cent to .1 per cent 
titanium as with ,15 per cent, showing that any excess of titanium over 
that required to produce oxidation is wasted; hence .05 per cent will 
be sufficient for foundry practice. 

He found that titanium reduces chill but the chill produced is very 
much harder than that made in the usual way. 

Titanium is of value as preventing blow-holes and producing sound 
castings. 

Vanadium 

Atomic weight 51.2 

Specific gravity 5.5 

Specific heat 

Melting point 4300° F. 

Latent heat of fusion 

Weight per cubic foot 344 pounds 



Vanadium 



269 



As a merchantable product this is obtained as ferrovanadium, con- 
taining from 10 to 15 per cent vanadium. 

The investigations of Dr. Richard Moldenke furnish about all that is 
so far known as to the action of this element on cast iron. The follow- 
ing table gives a summary of his experiments. 



c '3 



Analyses of test bars 



a w 

§21 



Burnt gray iron 


5 
3 



.05 






2.13 
2.03 


.094 
.09s 


.638 


.35 

.370 .... 


2 

7 


1310 
2220 


.090 
.100 


70 


Burnt iron, white 


3 
12 




•OS 




.50 


.41 


.146 


.423 


-43 

.65 .... 


II 

16 


1440 
1910 


.050 
.OS5 


33 






Machinery iron, gray. Melted pig iron. 


No scrap 







06s 



668 



24 



1980 
2070 
2200 
2740 
1970 
1980 
2130 
2372 
2530 
2360 



.105 
.105 
.115 
.130 
.100 
.xoo 
.100 
.090 
.120 
.100 







Remelted car wheels, white. No 


pig 


iron 
















.53 


122 


• 399 


.38 . 




82 








5 









.60 


138 




374 




44 




85 


1470 


050 




s 


•OS 






















2190 


050 


50 


7 


.10 
























2050 


050 


40 


8 


.15 
























2264 


060 


54 


4 

























.... 


2790 


070 


90 


6 




•OS 


00 




45 


096 




423 




40 


36 


113 


3020 


060 


los 


6 


.05 


•OS 


50 




66 


no 




591 


I 


150 


25 


117 


2970 


090 


100 


3 




.10 






45 


119 




414 




500 


31 


123 


2800 


055 


91 


4 




.10 


05 




53 


084 




431 




74 


27 


128 


3030 


090 


106 


6 




.IS . 






42 


112 




417 




40 


45 


133 


2950 


070 


100 


6 




.15 


SO 




SO 


082 




374 




54 


22 


137 


3920 


095 


166 



270 Influence of the Chemical Constituents of Cast Iron 

The vanadium alloy used contained : 

Vanadium 14.67 per cent; carbon 4.36 per cent; silicon 0.18 per cent. 

The analyses of the test bars show much more vanadium than was 
used. This is attributed to errors arising from the dif&culties experienced 
in making the experiments on too small a scale. 

Dr. Moldenke concludes: "The results shown in the table speak for 
themselves, and the averages tallied off for each table show a remarkable 
progression of values. To increase the breaking strength of a test bar 
from 2000 up to 2500 for gray iron and 1500 up to 3900 for white iron, 
is sufficient to warrant further investigation on the part of every foundry- 
man, who has special problems in strength to master." 

Thermit 

Thermit is a mixture of oxide of iron and aluminum, which when 
ignited burns at an intense heat (resulting temperature is said to be 
5400° F.) in consequence of the great affinity of aluminum for oxygen. 
This compound is made by the Goldschmidt Thermit Co. 

Its use in the foundry is to raise the temperature of dull iron; to keep 
the iron in risers fluid, and for the mending of broken castings. A 
titanium thermit is also made by same company. 

This is used for the introduction of titanium, to remove nitrogen and 
oxygen, as well as for its heating effect. The claim is made, that cast 
iron can be advantageously used in place of steel castings, if titanium 
thermit is employed in connection with it. Nickel thermit is used for 
the introduction of nickel. 

Oxygen 

Atomic weight ^5 • 9^ 

Specific gravity (compared to atmos- 
pheric air 32 °F. and one atmosphere) i . 1056 
Weight per cubic foot 624 . 8 grains 

No element, perhaps, causes the foundryman more trouble than 
oxygen. Iron oxidizes very rapidly at high temperatures, in presence of 
air. The oxides are readily dissolved in molten iron and the gases 
liberated from them in the castings are the frequent cause of cavities and 
blow-holes. 

Ferrous oxides, produced in the process of smelting, are found to a 
greater or less extent in all pig irons. Those irons in which mill cinder 
has been largely used, often contain high percentages of dissolved 
oxides. 



Nitrogen 271 

Frequently the ends of broken pigs present blow-holes in body of the 
pig, or worm-holes toward the upper surface. These are certain indi- 
cations of the presence of oxygen or sulphur and such iron should be used 
carefully. 

In remelting in the cupola, as the molten iron passes through the 
tuyere zone, more or less oxidation occurs, especially if the bed is high 
and the blast strong. 

Rusty scrap (fine scrap particularly) furnishes ferrous oxides in large 
amounts. 

The removal of ferrous oxides may.be largely effected in the cupola by 
an abundance of hot slag. 

Ferromanganese and aluminum are used in the ladle for same pur- 
pose. 

The most effective deoxidizers are the metals in the order named 
below : 

Titanium Aluminum 

Vanadium Sodium 

Magnesium Manganese 

Calcium Silicon 



Nitrogen 

Atomic weight 14.01 

Specific gravity (air i) . 9713 

Specific heat . 244 

Weight per cubic foot 548 . 8 grains 

Nitrogen is absorbed from the blast as a nitride, by iron in melting; 
and as the metal cools, the gas is Hberated. 

Very little is known as to the influence of nitrogen upon cast iron; its 
effect upon steel is very injurious; as little as .03 per cent causing a great 
loss in tensile strength and nearly eliminating ductility. Gray pig irons 
show only a trace of nitrogen from .007 to .009 per cent; in white iron 
it sometimes runs as high as .035 per cent. 

So far as tests have been made it does not appear that, in gray iron, 
any relation exists between the quality of the iron and the nitrogen 
content. 

It has a remarkably strong affinity for titanium, combining with it to 
form a nitride, which is insoluble in molten iron and passes off in the slag. 
Ground ferrotitanium previously heated is used in the ladle for removal . 
of nitrogen. 

Arsenic and copper are sometimes found in pig iron, but in amounts so 
small that the effects produced by them are inappreciable. 



272 Influence of the Chemical Constituents of Cast Iron 

In concluding the subject of metalloids, the statement made by Prof. 
Porter as to the approximate influence of the more important ones on 
combined carbon must not be omitted. 

I per cent silicon decreases combined carbon 45 per cent. 

I per cent sulphur increases " " 4. 50 per cent. 

I per cent manganese " " " 40 per cent. 

I per cent phosphorus " " " 17 per cent. 



CHAPTER X 
MIXING IRON 

The mixing of iron for the cupola is done either by fracture or by 
chemical analysis. 

Mixing by Fracture 

The fracture of the freshly broken pig is taken as the index of its com- 
position. A dark gray color, with coarse open crystalline grain indicates 
a soft iron, and, as a rule, one capable of carrying a large percentage of 
scrap. As the color becomes lighter and the grain closer, hardness 
increases and less scrap can be used. Very hard irons are mottled or 
white and are used for special work. 

A broken pig may present a dark fracture with open grain, but with a 
fine white streak showing at the outer edges of the fracture. Such an 
iron will make hard castings, owing to the presence of too much man- 
ganese. 

Blow holes and worm holes indicate sulphur or ferrous oxides. Iron 
showing these with frequency should be used carefully. 

Segregations, much lighter in appearance than the rest of the fracture, 
frequently appear. These indicate higher percentages of carbon, sulphur 
or manganese at those particular spots and the iron should be used 
with care. 

Mixing by fracture is uncertain and is liable to produce irregular and 
unsatisfactory results. 

The foundryman must always proceed cautiously and can only arrive 
at the results desired by careful trial. The following mixtures are taken 
from West's " Foundry Practice." 

Locomotive Cylinders 
2600 pounds car wheel scrap. 
600 pounds soft pig. 

Marine and Stationary Cylinders 
50 per cent No. i charcoal. 
50 per cent good machinery scrap. 
33 per cent car wheel scrap. 
33 per cent good machinery scrap. 
33 per cent No. i soft pig. 
273 



274 Mixing Iron 

Rolling Mill Rolls 
50 per cent car wheel scrap. 
25 per cent No. i charcoal. 
25 per cent No. 2 charcoal. 

Small Chilled Rolls 
1300 pounds old car wheels. 
100 pounds No. I charcoal. 
300 pounds steel rail butts. 

Kettles to Stand Red Heat 
1300 pounds No. I charcoal pig. 
800 pounds car wheel scrap. 
700 pounds good machinery scrap. 

Chilled Castings to Stand Friction {no strain) 
200 pounds white iron. 
200 pounds plow points. 
100 pounds No. 2 charcoal. 
100 pounds car wheel scrap. 

Ordinary Castings 

33 per cent No. i soft pig. 
67 per cent scrap. 

Thin Pulleys 

66 per cent No. i soft pig. 

34 per cent scrap. 

Sash Weight 

67 per cent scrap tin. 
33 per cent stove scrap. 

The advent of the chemist into the foundry offers means to avoid 
many of the uncertainties coming from the selection of irons by fracture, 
and the more advanced foundrymen are now -mixing their irons by 
analysis. 

Mixing Iron by Analysis 

This method of mixing iron is by no means entirely removed from 
uncertainties. The chemist is not yet able to insure the production, from 
irons of known chemical composition, of castings of definite physical 
characteristics. Analysis should be supplemented by physical tests. 

Again, while the foimdryman may have correct analysis of his pig iron, 
if scrap is used to any extent, especially foreign scrap, he must approxi- 
mate the elements contained therein. 



Mixing Iron by Analysis 



275 



The statements made on page 307 offer some little assistance, but, in 
general, reliance must be placed on experience in this respect. Where 
the scrap comes entirely from previous casts, one can readily arrive at 
its constituents and much uncertainty is removed. 

The quahties necessary for different grades of castings may be sum- 
marized as follows: 

1. Hollow Ware, Stove Plate, Sanitary Ware. — Require fluidity, 
softness; must be high in silicon and phosphorus; low in combined 
carbon. 

2. Light Machinery Castings. — Require fluidity, softness, strength 
and absence of shrinkage. Must be high in total carbon and manganese; 
low in sulphur and contain less silicon and phosphorus than grade No. i. 

3. Heavy Machinery Castings. — Require softness, strength and low 
shrinkage. Should be lower in silicon, phosphorus and graphitic carbon 
than No. 2. Higher in combined carbon and manganese; low in sulphur. 

4. Castings requiring great strength should be low in silicon, graphitic 
carbon, sulphur and phosphorus. Combined carbon should be about 
.50 per cent; manganese .8 per cent to i.o per cent. 

5. Car Wheels and Chilled Castings. — Require low silicon, phosphorus, 
graphitic carbon and sulphur. High combined carbon and manganese. 

6. Chilled Rolls. — Require low silicon, graphitic carbon and phos- 
phorus. High combined carbon. 

The following table is abstracted from "Proceedings of the American 
Foimdrymen's Association," Vol. X, Part II, which contains the results 
of a long series of tests made by their committee to standardize test bars. 
The mixtures are not given as being recommended by the committee for 
the several purposes, but simply to indicate the practice of some of the 
larger American foundries. 

Table II 



Character of work 


Silicon 


Sulph. 


Phos. 


Mang. 


Graph, 
carb. 


Total 
carb 


Remarks 


Ingot moulds 

Dynamo frames 

Light machinery 

Chilled rolls 


1.67 

1.95 

2.04 

.85 

.72 

.97 

3.19 

1.96 

2.49 

4.19 

2.32 

0.91 


.032 
.042 
.044 
.070 
.070 
.060 
.084 
.081 
.084 
.080 
.044 
.218 


I 
I 

4 


095 
405 
578 
482 
454 
301 
160 
522 
839 
236 
676 
441 


■ IS 
.17 
.40 
.38 
.48 

,■2 


.06 
.00 
3.43 
3.08 
2.99 
2.99 
.03 
2.62 


'2;36' 
3.04 
4.17 
3. .41 
3.32 
3.39 
2.88 
3.12 


Ton heat 
60 
60 
40 
30 






Car wheel iron 


15 

20 


Heavy machinery. . . 

Cylinder iron 

Novelty iron 

Gun iron . 


30 
10 
5 
10 


Sash weights 


IS 



276 



Mixing Iron 
Table III 



Automobile cylinders 


Silicon 


Sulph. 


Phos. 


Mn. 


Graph, 
carb. 


Total 
carb. 


25 per cent charcoal iron 


2.46 


.063 


• 531 


.063 









Transverse strength, 2901. 

At a later period Prof. J. J. Porter, at the request of the American 
Foundrymen's Association, undertook the investigation of the composi- 
tions used for various classes of castings, with a view to formulating 
standard mixtures. His report embraces every variety of work and 
contains tabulated analyses of several hundreds of mixtures in use. 
The averages of the mixtures in each class of work, together with those 
suggested by Prof. Porter, are subjoined. 

Acid-resisting Castings 



Mixture 


Silicon 


Sulphur 


Phosphorus 


Manganese 


Combined 
carbon 


Total 
carbon 


Average 


Per cent 

2.03 
1.00-2.00 


Per cent 

.033 
under .05 


Per cent 

.425 
under .40 


Per cent 

1. 13 
I. 00-1.50 


Per cent 


Per cent 
3 33 


Suggested 




3. 00-3. SO 


Agricultural Machinery, Ordinary 


Average 

Suggested 


2.33 
2.00-2.50 


.072 
.06-. 08 


.766 
.60-. 80 


.62 
.60-. 80 


.355 


3.45 


Agricultural Machinery, Very Thin 


Average 

Suggested 


2.70 
2.25-2.75 


.065 
.06-. 08 


■ 75 
.70-. 90 


.65 
.SO-. 70 


.20 


3. SO 


Air Cylinders 


Average 

Suggested. . . . 


1.28 
I. 00-1.75 


.084 
under .09 


.401 
.30-.50 


.69 
.70-. 90 


.633 


3.45 
3.00-3.30 






Ammonia Cylinders 


Average 

Suggested 


1. 55 
I. 00-1.75 


under .095 
lindpr OQ 


under .70 
.30-.50 


.70 
.70-.90 








3.00-3.30 











Mixing Iron by Analysis 
Annealing Boxes for Malleable Casting Work 



277 



Mkture 


Silicon 


Sulphur 


Phosphorus Manganese 


Combined 
carbon 


Total 
carbon 


Suggested 


Per cent 
.650 


Per cent 
• OS 


Per cent 
.10-. 20 


Per cent 
.20 


Per cent 
2.75 


Per cent 
2.75 



Annealing Boxes, Pots and Pans 



Average . . 
Suggested 

Average . . 
Suggested 

Average . . 
Suggested 

Average . . 
Suggested 

Average 
Suggeste 

Average.. 
Suggested 

Average . . 
Suggested 



1.52 
I . 40-1 . 60 



.043 
under .06 



under .20 



.69 
.60-1.00 



.58 



3.29 

low 



Automobile Castings 



1.93 
1.75-2.25 



•059 
under .08 



■ 52 

.4o-.5<^ 



.60-. 80 



.52 



Automobile Cylinders 



2.15 
1.75-2.00 



.091 
under .08 



.643 
.40-. so 



.46 
.60-. 8 



.45 
.55-. 65 



3.14 
3.00-3.25 



Automobile Flywheels 



2.73 
2.25-2.50 



under .07 



.475 
.4O-.50 



.625 
.50-. 70 



.335 







Balls for Ball Mills 






Average 

Suggested 


1. 00 
I. 00-1.25 


.10 

under .08 


.30 
under .20 


.50 
.60-1.0 




low 




low 







Bed-plates 



1. 815 
I. 25-1. 75 



.07 
under .10 



.535 
.3<>--5o 



.60 
.60-. 80 



.53 



Binders (see Agricultural Machinery) 
Boiler Castings 



2.38 
2.00-2 50 



.065 
under .06 



■ 41 
under .20 



.79 
.60-1.00 



278 Mixing Iron 

Car Castings, Gray Iron (see Brake Shoes and Car Wheels) 



Mixture 


Silicon 


Sulphur 


Phosphorus Manganese 


Combined 
carbon 


Total 
carbon 


Average 

Suggested.... 


Per cent 

2.03 
1.50-2.25 


Per cent 

.069 
under .08 


Per cent 

.65 

.40-. 60 


Per cent 

.62 

.60-. 80 


Per cent 

• 52 


Per cent 
3.50 


Car Wheels, Chilled 


Average 

Suggested. ... 


.642 
.60-. 70 


.094 
.08-. 10 


.38 
.30-. 40 


.44 
.50-. 60 


.80 
.60-. 80 


3.6s 
3.50-3.70 



Car Wheels, Unchilled (see Wheels) 

Chemical Castings (see Acid-resisting Castings) 

Chilled Castings 



Average . . . 
Suggested . 



1.04 
.75-1.25 



.105 
.08-0.10 



.40 
.20-. 40 



.76 
.80-1.2 



1.96 



3.19 



Chills 



Average . . . 
Suggested . 



2.07 
1.75-2.25 



.073 

under .07 



.31 

.20-. 4 



.60-1.00 



2.64 



Collars and Couplings for Shafting 



Average.. . 
Suggested . 



1.60 
1.75-2.00 



• 04 
under .08 



.55 

.40-. so 



• 55 
.60.-80 



3.57 



Cotton Machinery (see also Machinery Castings) 



Average . . . 
Suggested. 



2.25 
2.00-2.25 



under .09 
under .08 



.70 
.60-. 80 



.60 
.60-. 80 



3.45 







Crusher Jaws 








Average 

Suggested 


I. lb 
.80-1.00 


.127 .45 
.08-. 100 .20-. 40 


.92 
.80-1.20 


3.00 


3.125 



Cutting Tools, Chilled Cast Iron 



Average. . . 
Suggested . 



1.35 
I. 00-1.25 



.117 
under .08 



.60 
.20-. 40 



.54 
.60-. 80 



.65 



3.00 



Mixing Iron by Analysis 



279 



Cylinders 

See Air Cylinders Ammonia Cylinders 
Automobile " Gas Engine " 

Hydraulic " Locomotive " 

Steam Cylinders 

Cylinder Bushings, Locomotive (see Locomotive Castings) 
Dies for Drop Hammers 



Mixture 


Silicon 


Sulphur 


Phosphorus 


Manganese 


Combined 
carbon 


Total 
carbon 


Average 

Suggested.... 


Per cent 

1.40 
I. 25-1. 50 


Per cent 

.075 
under .07 


Per cent 

.25 
under .20 


Per cent 

.55 

.60-. 80 


Per cent 
1. 00 


Per cent 
3.20 






Diamond Polishing Wheels 


Average 


2.70 


.063 


.30 


.44 


r.60 


2.97 


Dynamo and Motor Frames, Bases and Spiders, Large 


Average 

Suggested 


2.025 
2.00-2.50 


.0655 
under .08 


.54 
.50-. 80 


.49 
.30-.40 


.56 
.20-. 30 


3.73 
low 


Dynamo and Motor Frames, Bases and Spiders, Small 


Average 

Suggested 


2.66 
2.50-3.00 


.073 
under .08 


.73 
.50-. 80 


.45 
.30-. 40 


.30 
.20-. 30 


3.4s 

low 


Electrical Castings 


Average 

Suggested 


2.30 
2.00-3.00 


.068 
under .08 


.62 .48 
.50-. 80 .30-. 40 


.48 
.20-. 30 


3.61 

low 



Eccentric Straps (see Locomotive Castings and Machinery Castings) 
Engine Castings 

See Bed Plates Engine Frames 

Flywheels Locomotive Castings 

Machinery Castings Steam Cylinders 

Engine Frames (see also Machinery Castings) 



Average.. . 
Suggested . 



1 72 


.09 


.48 


.60 


1.25-2.00 


under .09 


.3c^.5o 


.60-1.00 



28o 



Mixing Iron 



Fans and Blowers . (see Machinery Castings) 
Farm Implements 



Mixture 


Silicon 


Sulphur Phosphorus 


Manganese 


Combined 
carbon 


Total 
carbon 


Average 

Suggested.... 


Per cent 

2. OS 

2.00-2.50 


Per cent 

.078 
.06-.08 


Per cent 

.78 

.50-. 80 


Per cent 

.455 

.60-.80 


Per cent 
.48 


Per cent 
3.35 


Fire Pots 




2. so 
2.00-2.50 


under .07 
under .06 


under .20 
under .20 


.90 
60-1.00 






Suggested .... 




low 








Flywheels ( 


see also Automobile Flywheels and Machinery Castings) 




1.85 
i.so-2.25 


.09 
under .08 


.525 
.40-. 60 


.55 
.50-. 70 






Suggested 






Friction Clutches 


Average 


2.25 
1.75-2.00 


under .15 
.08-. 10 


under .70 
under ..30 


under .70 
.50-. 70 




low 








Furnace Castings - 




2.125 
2.00-2.50 


under .06 


.40 
under .20 


.51 
.60-1.00 






Suggested. . . . 




low 










Gas Engine Cylinders 


Average.. .... 

Suggested. . . . 


1. 18 
I. 00-1.75 


.082 
under .08 


.46 

.20-. 40 


.63 
.70-. 90 


• 93 


3.23 

3 00-3 30 








Gears, Medium 


Average 

Suggested 


1.92 
1.50-2.00 


.075 
under .09 


• 47 
.40-. 60 


.576 
.70-.90 


.55 


3.79 


Gears, Small 




2.72 
2.00-2.5© 


.08 
under .08 


■91 

.50-. 70 


.80 
.60-. 80 






Suggested 







Mixing Iron by Analysis 
Gears, Heavy 



281 



Mixture 


Silicon 


Sulphur 


Phosphorus 


Manganese 


Combined 
carbon 


Total 
carbon 


Average 


Per cent 

1.38 
I. 00-1.50 


Per cent 

.081 
.08-. 10 


Per cent 

• 39 

.30-. 50 


Per cent 

• 59 

.80-1.0 


Per cent 
.92 


Per cent 
3^33 
low 








Grate Bars 


Average . . 

Suggested 


2.38 
2.00-2.50 


.08 
under 1.06 










under .20 


.60-1.0 under .30 


low 


Chilled Castings for Grinding Machinery 


Average 

Suggested.... 


.50 

•SO-. 75 


.200 
.15-. 20 


.45 
.20-. 40 


1.50 
1.5-2.0 


300 


3.00 


Gun Carriages 


Average 

Suggested . . . 


.97 
I. 00-1.25 


• OS 
under .06 


.37 
.20-. 30 


.46 
.80-1.0 


.865 


2.73 

low 








Gun Iron 


Average 

Suggested.... 


1.09 

I.OO-I.2S 


.053 
under .06 


• 32 
.20-. 30 




.62 


.99 
.80-1.0 


306 

low 






Hangers for Shafting 


Average 

Suggested 


1.60 

1.50-2.00 


.04 
under .08 


• 55 
.40-. 50 


.55 
.60-. 80 


.30 


3.57 



Hardware, Light 


Average 

Suggested 


2.30 

2.25-2.75 


.06 
under .08 


• 74 
.5o-^8o 


.76 
.SO-. 70 


• 32 


3.39 


Heat-resisting Iron 


Average 

Suggested 


1.95 

1.25-2.50 


.056 
under .06 


.52 
under .20 


.68 
.60-1.00 


.46 
under .30 


3.46 

low 



282 



Mixing Iron 
Hollow Ware 



Mixture 


Silicon 


Sulphur 


Phosphorus 


Manganese 


Combined 
carbon 


Total 
carbon 


Average 

Suggested 


Per cent 

2. SI 
2.25-2.75 


Per cent 

1. 10 
under .08 


Per cent 

.62 

.50-. 70 


Per cent 

.41 

.50-. 70 


Per cent 
.24 


Per cent 
3.18 


Housings for Rolling Mills 


Average 

Suggested.... 


1. 125 

I. 00-1.25 


.085 
under .08 


.65 
.20-. 30 


.75 
.80-1.0 




low 




low 






Hydraulic Cylinders, Heavy 


Average 

Suggested 


1. 19 
.80-1.20 


.084 
under .10 


.39 
.20-. 40 


.82 
.80-1.0 


■ 99 


3.12 

low 






Hydraulic Cylinders, Medium 


Average 

Suggested 


1.67 
,1.20-1.60 


.071 
under .09 


.375 
.30-. 50 


.55 
.70-. 90 








low 






Ingot Moulds and Stools 


Average 

Suggested 


1.43 
I. 25-1. 50 


.046 .095 
under .06 under .20 


.345 
.60-1.0 














Locomotive Castings, Heavy 


Average 

Suggested .... 


1.55 
I. 25-1. 50 


.081 
under .08 


.50 
.30-. 50 


.56 
.70-. 90 


.60 


3.50 


Locomotive Castings, Light 


Average 

Suggested.... 


1.72s 
1.50-2.00 


.075 
under .08 


53 
.40-. 60 


.58 
.60-. 80 


.50 


3.50 


Locomotive Cylinders 


Average 

Suggested 


I.4S7 
I. 00-1.50 


.084 
.08-. 10 


.58 
.30-. 50 


.60 
.80-1.0 


.60 • 


3. so 



Mixing Iron by Analysis 



283 



Locks and Hinges (see Hardware, Light) 
Machinery Castings, Heavy 



Mixture 



Silicon 



Average 

Suggested. . . , 



Per cent 

1.335 
I. 00-1.50 



Sulphur 



Per cent 

.084 
under .10 



Phosphorus 



Per cent 

.43 

.30-. 50 



Manganese 



Per cent 

.58 

.80-1.0 



Combined 
carbon 



Per cent 
.33 



Total 
carbon 



Per cent 
3.21 

low 





Machinery Castings, Medium 






Average 

Suggested 


1.932 
i.so-2.00 


.078 
• under .09 


.61 
.40-. 60 


.53 
.60-. 80 


.47 


3.33 


Machinery Castings, Light 


Average 

Suggested 


2.57 
2.00-2.50 


.069 
under .08 


.74 
.50-. 70 


.52 
.50-. 70 


.27 


3.49 



Machine Tool Castings (see Machinery Castings) 
Motor Frames, Bases and Spiders (see Dynamo) 
Molding Machines (see Machinery Castings) 
Mowers (see Agricultural Castings) 

Niter Pots (see Acid-resisting Castings and Heat-resisting 
Castings) 

Ornamental Work 



Average 

Suggested.... 


2.95 

2.25-2.75 


.095 
under .08 


.84 
.60-1.0 


.54 
.50-. 70 


.135 


3.03 






Permanent Moulds 


Average 

Suggested.... 


2.085 
2.00-2.25 


.078 
under .07 


1 .075 
.20-. 40 


.35 
.60-1.0 


.485 


3.4s 


. 




Permanent Mould Castings 


Average 

Suggested 


2.5 
1.50-3.00 










350 


under .06 




under .40 


^ 








Piano Plates 


Average 

Suggested 


2.00 
2.00-2.25 


low- 
under .07 


.40 
.40-. 60 


.60 
.60-.80 











284 



Mixing Iron 
Pillow Blocks 



Mixture 


Silicon 


Sulphur 


Phosphorus 


Manganese 


Combined 
carbon 


Total 
carbon 


Average 

Suggested 


Per cent 

1.60 
I. 50-1. 75 


Per cent 

.04 
under .08 


Per cent 

.55 

.40- .50 


Per cent 

.55 

.60-. 80 


Per cent 
.30 


Per cent 
3.50 


Pipe 


Average 

Suggested 


2.00 
1.50-2.00 


.06 
under .10 


.60 
.50-. 80 


.60 
.60-. 80 










Pipe Fittings 


Average 

Suggested 


2.36 
I. 75-2. 50 


.084 
under .08 


.51 
.50-. 80 


.74 
.6c^.8o 


.70 


3.68 


Pipe Fittings for Superheated Steam Lines 


Average 

Suggested.... 


1.57 
I. 50-1. 75 


.078 
under .08 


.49 
.20-. 40 


.56 
.70-. 90 


.17 


2.90 






Piston Rings 


Average 

Suggested 


1. 61 
i.So-2.00 


.073 
under .08 


.72 
.30-. 50 


.45 
.40-. 60 


.53 








Plow Points, Chilled 


Average 

Suggested.... 


1. 15 
■75-1.25 


.086 
under .08 


.30 
.20-. 30 


.68 
.80-1.0 


2.10 


3.30 






Printing Presses (see Machinery Casting) 
Propeller Wheels 


Average 

Suggested 


1.28 
I.OO-I.7S 


low 
under .10 


.26 
.20-. 40 


• 455 
.60-1.0 


.60 








Pulleys, Heavy 


Average 

Suggested 


2.07 
I. 75-2. 25 


.05 
under .09 


.575 
.5<^.7o 


.575 
.60-. 80^ 


.30 


3.66 



Mixing Iron by Analysis 

Pulleys^ Light 



285 



Mixture 


Silicon 


Sulphur 


Phosphorus 


Manganese 


Combined 
carbon 


Total 
carbon 


Average 

Suggested 


Per cent 

2.55 
2.25-2.75 


Per cent 

.069 
under .08 


Per cent 

.695 

.60-.80 


Per cent 

.62 

.50-.70 


Per cent 
.35 


Per cent 
3.48 


Pumps, Hand 


Average 


2.52 
2.00-2.25 


under .08 
under .08 


.80 
.60-.80 


.40 
.50.-70 






Suggested 






Radiators 


Average 

Suggested.... 


2.30 
2.00-2.25 


low 
under .08 


.62 
.60-. 80 


.425 
•so-. 70 


.425 
.50- .60 


3.45 


Railroad Castings 


Average 

Suggested 


2.03 
1.50-2.25 


.065 
under .08 


.69 
.40-. 60 


.64 
.60-. 80 


.525 


3.50 


Retorts (see Heat-resisting Castings) 
Rolls, Chilled 


Average 

Suggested 


.73 
.60-. 80 


.055 
.06-. 08 


.534 
.20-. 40 


.74 
1. 0-1.2 


1.75 


3.12 
3.00-3.25 


Rolls, Unchilled {Sand Cast) 


Average 


.75 


.03 


.25 


.66 


1.20 


4.10 


Scales 


Average 

Suggested.... 


1.83 
2.00-2.30 




1.05 
.60-1.0 


1.43 
.50-. 70 






under .08 










Slag Car Castings 


Average 

Suggested 


1.88 
1.75-2.0 


.058 
under .07 


.67 
under .30 


.79 
.70-.90 


. .56 


3.68 







286 



Mixing Iron 



Smoke Stacks, Locomotive (see Locomotive Castings) 
Soil Pipe and Fittings 



Mixture 


Silicon 


Sulphur 


Phosphorus 


Manganese 


Combined 
carbon 


Total 
carbon 




Per cent 

2.00 
1.75-2.25 


Per cent 

.060 
under .09 


Per cent 

1. 00 
•SO-. 80 . 


Per cent 

.60 

.60-80 


■ Per cent 


Per cent 


Suggested 







Steam Cylinders, Heavy 


Average 


1.20 

I.OO-I.2S 


.091 

under .10 


.36 
.20-. 40 


.50 
.80-1.0 


.81 


3.35 








Steam Cylinders, Medium 


Average 

Suggested 


1.658 
I. 25-1. 75 


.082 
under .09 


.55 
.30-. 50 


.61 
.70-. 90 


.62 


3.43 


Steam Chests (see Locomotive Castings and Machinery Castings) 
Stove Plate 


Average 

Suggested 


2.77 
2.25-2.75 


.076 
under .08 


.82 
.60-. 90 


-59 
.60-. 80 


.28 


3.33 


Valves, Large 




1.34 
I. 25-1. 75 


.095 
under .09 


.43 
.20-. 40 


.64 
.80-1.0 






Suggested 










Valves, Small 


Average 

Suggested 


1.96 ' 

1.1 5-2. 2S 


.067 
under .08 


.585 
.30-. 50 


.705 
.6<^.8o 


1. 16 


4.18 
low 








Valve Bushings (see Locomotive Castings and Machinery Castings) 
Water Heaters 




2.15 
2.00-2.25 


.050 
under .08 


.40 
.30-. so 


• SO 
.6<^.8o 






Suggested 







Mixing Iron by Analysis 



287 



Weaving Machinery (see Machinery Castings) 
Wheels, Large 



Mixttire 


Silicon 


Sulphur 


Phosphorus 


Manganese 


Combined 
carbon 


Total 
carbon 


Average 


Per cent 

2.10 
1.50-2.00 


Per cent 

.04 
under .09 


Per cent 

.40 
.30-. 40 


Per cent 

.70 
.60-.80 


Per cent 


Per cent 


Suggested 











Wheels, Small 








Average 


1.8s 
I. 75-2. 00 


.0665 
under .08 


.50 
■40-. 50 


• 45 
.50-. 70 






Suggested 







Wheel Centers (see Locomotive Castings) 
White Iron Castings 



Average. 



.70 



.33 



2.90 



Wood Working Machinery (see Machinery Castings) 
Brake Shoes 



Average.. . 
Suggested. 



1-94 
I. 40-1. 90 



.125 
.08-. 10 



.675 
.30 



.556 
.50-. 70 



.53 



3.16 
low 



Knowing the desired analysis for any class of casting to be made, the 
simplest way to arrive at the amounts of the different irons to be used 
is by percentage. For example, let the requirements be for an iron to 
produce machinery castings of which the analysis shall be: 



Silicon 


Sulphur 


. Phosphorus 


Manganese 


2.00 


.084 


.350 


.62s 



As previously stated, the loss in silicon in remelting will be from 10 
to 20 per cent, the same for manganese, and a gain of .03 in sulphur, 
phosphorus remainuig constant. The mixture then must contain: 



Silicon 


Sulphur 


Phosphorus 


Manganese 


2.22 


.054 


.350 


.687 



288 Mixing Iron 

The irons then available are: 





Silicon 


Stilphur 


Phosphorus 


Manganese 


No. 2 Southern . 


2.25 
2.IO 
4.20 

I. go 


.04 
.02 
.02s 
.080 


.280 
.350 
.820 
.284 


735 * 


No. 2 Northern . . . 


940 


Si] ver gray 

Scrap 


.820 
.540 



After two or three trials it is found that the desired mixture may be 
obtained from 





Silicon 


Sulphur 


Phosphorus 


Manganese 


20 per cent No. 2 Southern, giving 
20 per cent No. 2-Northern. giving 
10 per cent silver gray, giving . . . 
50 per cent scrap, giving 


.450 
.420 
.420 
.950 
2.240 


.008 
.004 
.0025 
.0400 

.0545 


.056 
.070 
.082 
.142 
.350 


.147 
.188 
.082 
270 




.687 



Example 2. — Required an iron for pulleys and light castings of 
following analysis: Silicon, 2.40; sulphur, .09; phosphorus, .700; 
manganese, .52, and to carry 50 per cent scrap. 

Available irons: 



No. 2 Southern 
No. 2 Northern 

Silver gray 

Scrap 



Silicon 



2.72 
2.40 
5.00 
2.20 



Sulphur 



.070 
.020 
.024 



Phosphorus 



.750 
.600 
.960 
.660 



Manganese 



.56 
.53 
.62 



Correcting for losses of sihcon and manganese and gain of sulphiu: the 
mixture must contain silicon, 2.66, sulphur, .06, phosphorus, .70, man- 
ganese, .577. 

For reasons of economy no more than 10 per cent of the silver gray 
iron should be used. This with the 50 per cent scrap supplies: 





Silicon 


Sulphur 


Phosphorus 


Manganese 




• so 
1. 10 
1.60 

1.066 


.0024 

.040 

.0424 

.0176 


.096 
.330 
.426 

.274 


.053 




.310 


To be supplied by remaining pig 
iron . ... 


.363 
.214 







Mixing Iron by Analysis 



289 



By trial it is found that the remaining amounts of the different elements 
may be obtained by using: 



25 per cent No. 2 Southern 

15 per cent No. 2 Northern 

Giving 



Silicon 



Sulphur 



.0175 
.0030 
.0205 



Phosphorus 



.1875 
.0900 

.2775 



The sUght discrepancies of .02 silicon, .0029 sulphur, .0035 phosphorus 
and .01 manganese may be neglected. 

Where the scrap is very nearly of uniform quality, the analysis of the 
castings from any given heat furnishes data from which a very close 
approximation can be made of the scrap used in the previous heat. 

Assuming such character of scrap, and knowing the mixture used in 
any heat as well as the analysis of the castings, compute the analysis of 
scrap used in previous heat. 

Let the castings show the analysis of example 2, viz.: Si, 2.40, S, .09, 
P, .70, Mn, .52. Then the] mixture must have been as before, Si, 2.66, 
S, .06, P, .70, Mn, .577. 

The irons having the assumed analysis of example 2, then: 



25 per cent No. 2 Southern gives. 
15 per cent No. 2 Northern gives. 
10 per cent silver gray gives . . 



Which subtracted from the mix- 
ture leaves 



Silicon Sulphur Phosphorus Manganese 



.68 

.36 

■ 50 

1. 54 

1. 12 



.0175 
.0030 
.0024 
.0229 

.0371 



.1875 
.0900 
.0960 
.3735 

.3265 



■ 053 
.257 

.320 



As 50 per cent scrap was used, the analysis of scrap from previous heat 
is Si, 2.24, S, .0742, P, .653, Mn, .64, giving a very close approxima- 
tion. 



CHAPTER XI 



USE OF STEEL SCRAP IN MIXTURES OF CAST IRON 

Steel scrap, when added to mixtures of cast iron in quantities varying 
from lo to 40 per cent, closes the grain, increases the toughness and adds 
greatly to the tensile strength of the castings made from such mixture. 

The steel should be low in carbon, such as boiler plate scrap, machine 
steel, rail ends, etc. 

Turnings from machine steel are frequently used in the ladle. In this 
case the steel should be heated quite hot, placed in the ladle and the iron 
tapped out on it. The mixture should be thoroughly stirred until the 
steel is melted. In all cases the iron must be very hot. 

Mixing steel in the ladle does not give as satisfactory results as mixing 
in the cupola. 

As the steel is low in carbon the iron used should be high in total carbon, 
otherwise the castings will be hard with over 10 per cent steel scrap. 

The following table by Mr. H. E. Diller presents the results of a series 
of tests, with mixtures made by varying in percentages of steel scrap from 
i2i/^ to 37!/^ per cent: 



No. 


Sili- 
con 


Sul- I 
phur 


'hos- 
hor- '^ 
us ga 


lan- 

nese 


Comb, 
carbon 


Graph- 
itic 
carbon 


Total 
carbon 


Tensile 
strength 


Trans- 
verse 
strength 


Per 

cent 
steel 


I 


1.43 


.047 


564 


82 


.670 


3.14 


3.81 


23,060 


2550 





2 


1.50 


.065 


532 


33 


.640 


3-44 


3 


08 


30,500 


2840 


25 


3 


1.76 


.062 


488 


53 


.510 


3.12 


3 


63 


22,180 


2440 





4 


1.76 


.139 


51S 


57 


.430 


2.94 


3 


37 


37,090 


2770 


I2l/^ 


5 


1.77 


.069 


339 


49 


.560 


2.87 


3 


43 


32,500 


3120 


.121/^ 


6 


1.83 


.100 


610 


55 


.510 


2.44 


2 


95 


36.860 


3280 


25 


7 


1.75 


.089 


598 


35 


.740 


2.12 


2 


86 


30,160 


3130 


37^ 


8 


1.96 


.104 


446 


44 


.630 


3.18 


3 


81 


21,950 


2230 





9 


2.12 


.037 


410 


26 


.380 


3.26 


3 


64 


21,890 


3470 


121.^ 


10 


2.16 


.060 


31S 


20 


1.060 


2.30 


3 


36 


26,310 


2670 


12H 


II 


1.97 


.093 


470 


48 


.570 


2.83 


3 


40 


32,530 


3050 


2n\'i 


12 


2.35 


.061 


515 


56 


.540 


340 


3 


94 


21,990 


2200 





13 


2.53 


.104 


490 


54 


.600 


2.56 


3 


16 


33,390 


2850 


25 


14 


2.36 


.064 


327 


24 


1.080 


2.15 


3 


23 


31,560 


3200 


25 



These tests were made with pig iron, ferrosilicon and steel scrap. No 
cast iron scrap was used. Mr. Diller concludes: "The tests given seem 

290 



Recovering and Melting Shot Iron 



291 



to indicate that 25 per cent of steel will add 50 per cent to the strength of 
the iron, and 12K2 per cent of steel, approximately 25 per cent." 

The tests containing 371/^ per cent steel were hardly as much im- 
proved in strength as those with 25 per cent of steel; from which we may 
infer that the limit of the amount of steel it is beneficial to melt with 
iron in a cupola is between 25 and 371/i per cent. 

Results of experiments made by Mr. C. B. McGahey are embodied 
below. 

Mr. McGahey used test bars i in. by i in. by 24 in. (distance between 
supports not stated). 



No. 


Sili- 
con 


Sul- 
phur 


Phos- 
phor- 
us 


Man- 
ganese 


Per 

cent 
steel 


Depth 

of 
chill 


Trans- 
verse 
strength 


Remarks 


I 
2 
3 
4 


.82 
.88 
.58 
■ 79 


.097 
.081 
.097 
.081 


.23 
.24 
.25 
.239 


.54 
.67 
• 44 
.64 


7 
20 
23 
21.50 


In. 
.38 
.40 
.48 


1800 
2200 
2250 


Entirely gray when 
cast in sand. 
Depth of chill % in. 
Steel scrap (struc- 
tural shapes). 



"I find that to get the strongest bars I have to keep pretty close to 
these analyses and have made my strongest bar at 2350 pounds with 
.55 inch deflection. The iron had a fine grain, was low in graphite, but 
machined nicely. 

When ferromanganese was used, about i per cent was found to be 
best. The above resulting compositions (the silicons of the mixtures 
being calculated to bring them about right) are intended for castings 
ranging from i inch to 2}^ inches in section. 

Should heavier work be required it is better to run the silicon in the 
pig up to 2.75 and manganese up to 2.00 and use 33!/^ per cent of steel 
scrap." 

An addition of 10 per cent steel scrap to mixtures for engine cylinders 
gives excellent results affording a close-grained tough iron. Steel scrap 
increases shrinkage and causes the iron to set quickly; hence the irons 
used, should be high in total carbon and must be melted and poured very 
hot. 

Steel scrap promotes chill and is largely used with coke irons in making 
car wheels, obviating the use of the expensive charcoal mixtures. 

The charges containing steel should be melted during the first part 
of the heat, and in each charge the steel should precede the iron. 

Recovering and Melting Shot Iron 

The shot from gangways and cupola bottom is usually recovered by 
riddling the gangway sand; picking over the dump and by grinding the 



292 Use of Steel Scrap in Mixtures of Cast Iron 

bottom in the cinder mill. This is also done by magnetic or hydraulic 
separators. The amount recovered by machines is much greater than 
that obtained by hand. 

After charging of the cupola is completed, the shot should be thrown 
on top of the last charge, using with it some of the coke picked from the 
dump. Each heat should take care of the shot from the previous one. 

The melted iron coming from the shot can be poured into grate bars, 
sash weights, or other coarse castings; or it may be run into pigs and 
used as scrap. 

Mr. W. J. Keep describes his method of recovery as follows: ''After 
the blast has been shut off and all of the melted iron has been drained 
from the cupola, make a dam on the floor in front of the cupola spout 
about 4 inches high, enclosing a semicircular space, having a radius of 
about 4 feet. Let the melter lay a tapping bar across the spout and have 
three or four laborers with a piece of old iH inch shafting about 8 feet 
long ram in the breast. If the bottom and spout have been made right 
there will be no melted iron in the cupola, but ram back and forth to 
allow all to drain out. 

All the liquid slag in the cupola will run into the enclosed space 
underneath the spout and if there is any iron in this, it will run through 
the slag and lie on the floor in the form of a slab which can be picked up 
the next morning. 

When the cupola has been emptied of all slag and iron drop the 
bottom. I like to draw the refuse out from underneath the cupola, 
turning it- over and cooling it down with water. The pieces of the sand 
bottom are thrown to one side and all the iron that can be seen is picked 
up. All the iron taken from the cupola dump, the pig bed, or from the 
gangways, which is not bad casting, is weighed up and charged as remelt 
or home scrap. 

All remaining small pieces of coke, iron or slag are shoveled up from 
the bottom and from all parts of the foundry and placed in boxes on the 
cupola platform. This includes skulls from the ladles which contain 
more or less iron. 

When the last charge of iron has been placed in 'the cupola and the 
heat is near enough to the end to show that there will be no shortage of 
iron, throw into the cupola any shot iron that may be left over, and all 
the refuse previously mentioned. The iron and slag will be melted at 
once and the small bits of coke will hold the blast down and insure hot 
iron. 

All the finest shot iron is saved in this way, as well as all coke in the 
form of small pieces and nothing is lost." 

The disposition on the part of many foundrymen is to neglect the 



Melting Borings and Turnings 293 

saving of shot iron, preferring to sell to junk dealers what can be readily 
recovered. Such will not be the case, however, in a well- managed foundry, 
as by close attention to its recovery the loss in melt can be reduced 
from I to 2 per cent. 

At one of the large western foundries, through mismanagement, shot 
had been allowed to accumulate until a portion of the yard was covered 
to a depth of from 12 inches to 20 inches. This was dug up, milled and 
melted; 1500 pounds, at each heat, were thrown on top of the last charge, 
without additional fuel; the melted iron was run into pigs. 

Over 84 tons of No. 4 pig were recovered; 25 per cent of the scrap used 
in charging was replaced by this iron and the usual mixture was in no 
other respect changed. 

Burnt Iron 

This class of iron is of no use except for making sash weights. When 
used for ordinary purposes, the loss caused is greater than the gain. It 
makes iron hard, causes a great amount of slag and chokes up the cupola. 
It should be carefully selected and thrown out of the scrap. 

Melting Borings and Turnings 

Cast iron borings and turnings which are usually disposed of to junk 
dealers at a low price may be advantageously melted by packing them 
in wood or iron boxes, about 100 pounds to the box. 

The boxes should be charged a few at a time, by throwing them into 
the center of the charge and covering them with scrap. These will 
descend to near the melting zone before they are burned or melted. 

Mr. W. F. Prince has patented a process for melting borings, etc., 
which consists of packing them in sheet iron pipes, with or without 
bottoms. The pipes are of any convenient length, from 30 to 48 inches; 
the first one is placed on the coke bed and the others on top of it, with 
the charges surrounding them. 

This differs little from the method of using boxes, where the latter are 
piled on each other. In either case the containers prevent the fine 
material from being blown out of the stack. 

Many attempts have been made to render borings, etc., suitable for 
melting, by briquetting. So far, these efforts seem to have been only 
partially successful. 

A process has recently been developed in Germany, by which the 
borings are made into briquettes under hydraulic pressure. It is claimed 
that the product successfully meets the purpose and preliminary tests 
made in America seem to warrant the statement. 



CHAPTER XII 

TEST BARS 

TfflS subject has been treated exhaustively by a Committee of the 
American Foundrymen's Association. Their report was adopted by 
the Association in June, 1901. 

Extensive extracts from the report are given below. 

The work covered the testing of 1229 bars by 160 1 tests; the following 
table shows the character of the heats from which the bars were taken. 



Series 



A* 
B 
C 
D 

E 

Ft 

G 

H 

I 

J 

K 

L 



Class of iron 



Ingot mould 

Dynamo frame. . . . 
Light machinery . . 

Chilled roll 

Sand roll 

Sash Weight 

Car wheel 

Stove plate 

Heavy machinery. 

Cylinder 

Novelty 

Gun metal 



Melted in 



Cupola 

Cupola 
Air furnace 
Air furnace 

Cupola 

Cupola 
Cupola 
Cupola 
Cupola 
Cupola 
Cupola 
O. H. furnace 



Pig iron used 



Coke 
Coke and charcoal 
Coke and charcoal 
Cold-blast charcoal 
Warm-blast char- 
coal 
Coke and charcoal 
Coke and charcoal 

Coke 

Coke 

Coke 

Coke 
Coke and charcoal 



Size 






of 


Si 


P 


heat 






tons 






60 


1.67 


.095 


60 


1.95 


■ 40s 


40 


2.04 


.578 


30 


.85 


.482 


30 


.72 


.454 


15 


• 91 


• 441 


10 


• 97 


.301 


20 


3.19 


1. 160 


30 


1.96 


.522 


10 


2.49 


.839 


5 


4.19 


1.236 


10 


2.32 


.676 



.032 

.042 
.044 

.070 
.070 

.218 

.060 

.084 
.081 
.084 
.080 
.044 



* All pig iron. 

t Nearly all burnt scrap, originally from charcoal and coke iron. 

"Throughout the whole line of operations only regularly constituted 
mixtures were used, the balance of the heats from which these test bars 
were cast going directly into commercial castings of the classes designated. 
The results are, therefore, entirely comparable with daily practice. 

For purposes of comparison green sand and dry sand bars were made 
side by side. 

It was felt that comparison records were wanted just as much as 
specifications for the separate lines of product. For this reason, we 
recommend one standard size of test bar for comparative purposes only, 
each class of iron being given its special treatment for the information 
wanted in daily practice in addition. 

294 



Test Bars 



295 



"Our studies on the shape of the test bar have resulted in the selection 
of the round form of cross section and this mainly on the score of great- 
est uniformity in physical structure. . . . There is still a further 
point of interest, in the preparation of test bars and that is, the making 
of coupons from which the quality of the castings to which they are 
attached is to be judged. This method is used extensively in govern- 
ment work and in the making of cyl- 
inder castings. 

The idea of obtaining material 
from the same pour in the same 
mould as part of the casting itself is 
good enough in theory. Unfortu- 
nately, however, this direct connec- 
tion introduces elements of segrega- 
tion and temperature changes in the 
cast iron which make this test less 
valuable than is generally supposed. 
At best the iron which has passed 
through the different parts of a 
mold before entering the space for 
the coupon will not be representa- 
tive of the whole body, but rather 
one portion of it only. We therefore 
recommend the method shown later 
on in Fig. 75. The metal can be 
poured from crane or hand ladle, 
clean and speedily, and possesses the 
temperature of the average iron in 
the casting more nearly than the 
coupon method now practiced. 

Your committee while giving spe- 
cifications for the tensile test of cast 
iron is of the opinion that the trans- 
verse test is the more desirable and certainly within reach of even the 
smallest foundry. 

In selecting the test bars for the purpose of specification, we have 
followed the cardinal principle of selecting the largest cross section for 
the iron consistent with a sound physical structure and within the range 
and structural limits of an ordinary testing machine. 

The following are the sizes of bars selected for tests as a result of 
our investigations. 

For all tensile tests, a bar turned to .8 inches in diameter, corre- 





FiG. 75. 



296 Test Bars 

spending to a cross section of Yi square inch. Results, therefore, multi- 
phed by two, give the tensile strength per square inch. 

For transverse test, of all classes of iron for general comparison; a 
bar ii-i inches in diameter, on supports, 12 inches apart; pressure applied 
in the middle and deflection noted. 

Similarly for ingot mould, light machinery, stove plate and novelty 
iron, a ii.^-inch diameter bar; that is to say, for irons running from 2 per 
cent in silicon upward, or from 1.75 per cent silicon upward where but 
little scrap is in the mixture. 

For dynamo frames, sash weights, cylinders, heavy machinery and 
gun metal irons; similarly, a 2-inch diameter bar is recommended, that 
is, for irons running from 1.5 per cent to 2 per cent in silicon or where 
the silicon is lower and the proportion of scrap is rather large. 

For roll irons, whether chilled or sand, arid car wheel metals, a 214- 
inch diameter bar is recommended; that is, for all irons below i per cent 
silicon and which may, therefore, be classed as the chilling irons. 

The method of moulding the test bar we would recommend is given 
herewith. 

At least three bars of a kind should be made for a given test. 

The sand should not be any damper than to mould well and stand the 
wash of the iron without cutting, blowing or scabbing. It should be 
rammed evenly to avoid swells and poured by dropping the metal from 
the top through gates, or from ladle direct into the open mould. 

After the bars are cast they should remain in their moulds undis- 
turbed until cool." 

Proposed Standard Specifications for Gray Iron Castings 

1. Unless furnace iron, dry sand, loam moulding, or subsequent 
annealing is specified, all gray iron castings are understood to be of 
cupola metal; mixtures, moulds and methods of preparation to be fixed 
l>y the founder to secure the results required by purchaser. 

2. All castings shall be clean, free from flaws, cracks and excessive 
shrinkage. They shall conform in other respects to whatever points 
may be specially agreed upon. 

3. When the castings themselves are to be tested to destruction, the 
number selected from a given lot and the tests they shall be subjected to 
are made a matter of special agreement between founder and purchaser. 

4. Castings under these specifications, the iron in which is to be 
tested for its quality, shall be represented by at least three test bars cast 
from the same heat. 

5. These test bars shall be subjected to a transverse breaking test, 
the load applied at the middle with supports 12 inches apart. The 



Patterns for Test Bars of Cast Iron 



297 



breaking load and deflection shall be agreed upon specially on placing 
the contract, and two of these bars shall meet the requirements. 

6. A tensile strength that may be added, in which case at least three 
bars for this purpose shall be cast with the others, in the same moulds 
respectively. The ultimate strength shall also be agreed upon specially 
before placing the contract and two of the bars shall meet the require- 
ments. 

7. The dimensions of the test bars shall be as given herewith. There 
is only one size for the tensile bar and three for the transverse. For the 
light and medium weight castings the i^i inch D bar is to be used; 
for heavy castings, the 2 inch D bar; and for chilling irons the 2H inch 
n test bar. 

8. When the chemical composition of the castings is a matter of 
specification, in addition to the physical tests, borings shall be taken 
from all the test bars made; they shall be well mixed and any required 
determination (combined and graphitic carbon alone excepted), made 
therefrom. 

9. Reasonable facilities shall be given the inspectors to satisfy them- 
selves that castings are being made in accordance with specifications, 
and if possible tests shall be made at the place of production prior to 
shipment." 

Patterns for Test Bars of Cast Iron 



PfC* 



For Transverse Test 



U-2-- 



W t- 



■='^v 



/3' 



(MC^^ 



^-2i"-y^ 



loi'- 



For "^y?* Tensile Test 






Fig. 76. 



h2|-"*l 



1"^ 



±:^i::i, 



Steel Socket for Tensile Test of Cast Iron. — Two required 



k- 



1 



13" >l 



Standard Test Bar for Cast-iron Tensile Test. — Cross section equals 

J^ sq. in.; test piece shovdd fit loosely in socket 

Fig. 77- 



298 Test Bars 

Modulus of Rupture in Pounds Per Square Inch 

The report of the committee is accompanied by a table giving the 
moduli of rupture per square inch for bars under the various con- 
ditions of the tests and from H square inch to 16 square inches. It was 
found that, with few exceptions, the values decrease as the areas 
increase. 

In the table on pages 299 and 300, which is extracted from their 
report, the moduli are given for bars having areas of i square inch, 
2.25, 4, and 9 square inches. 

"The results show that rough bars are stronger than machined and 
that there is practically no difference between bars made in green or dry 
sand. 

An examination of the table shows that the transverse strength is 
greater in the rough than machined bars, except in two instances, viz. : 
D bar, series /, in dry sand the rough bar broke with 178 pounds less 
load than the machined bar. O bar, series L, in dry sand, the rough 
bar broke with 115 pounds less load than did the machined bar. The 
average loss in transverse strength of the green sand bar by machining 
was 12 per cent; that of the dry sand bar 10 per cent. 

The following articles are introduced as showing how little reliance 
can be placed on the results from test bars. It is shown that bars 
identical in chemical composition, but made from different brands, differ 
widely in physical properties; indicating the importance of using in 
mixtures, irons from different localities, as well as from different furnaces. 
The micrographs show clearly the variation in structure corresponding 
to the widely varying results, but it remains for the metallurgist to point 
out the causes for these differences." 

Erratic Results — Test Bars 

Mr. F. A. Nagle submitted to the American Society of Mechanical 
Engineers the following report of his investigation of test bars for castings 
used in the Baltimore Sewage pumps. 

"In machinery castings as well as in cast pipes, separate bars are cast 
and subjected to tensile or transverse stress to the breaking point, these 
results being used as evidence of compliance with the contract speci- 
fications. The writer has examined a large number of such test bars for 
castings used in the Baltimore Sewage pumps and here reports the results 
of this examination and study. 

Perhaps the most important conclusion is that the test bar is not to 
be regarded with too much confidence as indicative of the exact strength 
of the casting. All transverse bars were nominally 2 inches by i inch by 



Modulus of Rupture in Pounds Per Square Inch 299 





Rough 


Machined 


Area in 
square 


Square 


Round 


Square 


Round 


inches 


Green Dry 
sand sand 


Green 
sand 


Dry 

sand 


Green 
sand 


Dry 
sand 


Green 
sand 


Dry 
sand 



Ingot Mould Iron. Series A. Silicoti 1.67 



1. 00 


37.140 


27,530 


44.210 


33.660 


43.200 


38,610 


26,100 


27,840 


2.25 


32,880 


31.320 


34.S70 


33.870 


29.340 


30,790 


39,810 


38.120 


4.00 


29.540 


25,550 


34.900 


31.610 


31.150 


26,500 


34.320 


32,290 


9.00 


26,200 


21,180 


27,280 


26,540 


26,980 


21,690 


26,030 


28,660 





Dynamo Frame Iron. 


Series B. Silicon 1.95 




1. 00 


39.220 


38,380 


44,300 


49,160 


37,440 


30,240 


40,020 


39.150 


2.25 


39.540 


34,900 


41.270 


44,840 


36.670 


36,180 


44.790 


37.800 


4.00 


33.960 


34,460 


41,680 


39.230 


34.750 


33,250 


38,750 


37.270 


9.00 


29,680 


30,050 


35,600 


35.620 


32,740 


30,880 


35,400 


32,810 



Light Machinery Iron. 


Series C. Silicon 2. 


04 


37.000 
32,880 
36,170 
30,980 


39.190 
38.780 
34.550 
29.230 


48.050 
38,890 
42,560 
38,080 


50.380 
43.950 
40,150 
37.780 


40,230 
36,990 
33.290 


38,880 
35.420 
32,710 


55.680 
47,340 
42,920 
36.520 



1. 00 
2.25 
4.00 
9.00 



47,850 
SI. 350 
37,550 
36,290 



Chilled Roll (Furnace). Series D. Silicon 0.85 



1. 00 
2.25 
4.00 
9.00 



44,120 
47.760 
46,710 
52,700 



44,010 

67,680 
43.260 
54,910 


49.440 
69.130 
65,940 
65.850 


49.850 
59.010 
75.000 
51,660 









1. 00 
2.25 
4.00 
9.00 



Sand Roll Iron (Furnace). Series E. Silicon 0.72 



51,560 


44,180 


51.620 


48,740 








41.740 


46,290 


41.420 


41,960 








34,700 


33,720 


55.110 


61,770 








33,040 


35.760 


53.540 


55,440 









Sash Weight Iron. Series F. Silicon 0.91 



1. 00 
2.25 
4.00 
9.00 



52,920 
59.170 
61,870 
42,710 



42,540 
51,130 

SI, 810 

39,160 



58,430 


50,050 








39,840 


S3,oio 








50,130 


47.090 








42,370 


4S,73o 









300 



Test Bars 





Rough 


Machined 


Area in 
square 


Square 


Round 


Square 


Round 


inches 


Green 
sand 


Dry 
sand 


Green 
sand 


Dry 

sand 


Green 
sand 


Dry 
sand 


Green 
sand 


Dry 
sand 



Car Wheel Iron. Series G. Silicon 0.97 



1. 00 


47,110 


44,810 


52,600 


61,720 


43,200 


46,080 


64,380 


52,200 


2.25 


32,120 


28,200 


45,880 


39,740 


44,640 


40,680 


43,200 


46,170 


4.00 


35,460 


32,190 


45,970 


39,330 


27,520 


32,760 


41.590 


37 .350 


9.00 


32,050 


32,140 


37,610 


35,150 


28,730 


28,960 


33,930 


28.040 



Stove Plate Iron. Series H. Silicon 3.19 



1. 00 


27,980 


29,360 


42,570 


36,920 


48,960 


43,200 


78,300 


68,600 


2.25 


24,960 


30,710 


42,160 


41,420 


22,500 


24,480 


33.250 


31,550 


4.00 


27,980 


28,930 


40,540 


36,940 


23,400 


28,SlO 


32,290 


21,910 


9.00 


25,620 


25,020 


33,350 


33,550 


23,710 


24,100 


25,540 


23,000 





Heavy Machinery Iron 


. Series I. Silicon! 


96 




1. 00 


36,000 


44,060 


53,210 


54,180 


43,200 


46,080 


52,200 


55,680 


2.25 


35,290 


35,040 


43,860 


47,100 


33,120 


39,060 


44,900 


43,200 


4.00 


36,120 


33,580 


42,290 


41,330 


30,400 


32,970 


41,670 


42,420 


9.00 


23,850 


20,880 


33,040 


34,970 


37,040 


30,410 


36,030 


38,02a 







Cylinder Iron. Series J. 


Silicon 2.49 






1. 00 


43,350 


34,270 


51,690 


55,500 


39,790 


39,790 


52,200 


46,980 


2.25 


30,880 


31,950 


33,400 


41,900 


39,960 


38,520 


51,040 


53.160 


4.00 


32,600 


30,420 


43,180 


41,320 


26,400 


26,610 


38,110 


38,240 


9.00 


27,830 


25,630 


40,900 


40,170 


26,400 


24,890 


34.470 


34.310 



Gun Iron (¥vjnidi.c€). Series L. Silicon 2.^,2 







Novelty Iron. Series K. 


Silicon 


4.19 






1. 00 


25.430 


36,490 


39,040 


42,530 










2.25 


25.640 


26,290 


37,760 


37,670 










4.00 


27,120 


26,860 


33,550 


34,560 










9.00 


22,220 


24,130 


30,890 


32,520 











1. 00 


52,230 


44,030 


71,570 


67,350 


53,270 


50,400 


80,040 


71.340 


2.25 


49,290 


46,760 


67,060 


66,140 


47,520 


39.600 


59.040 


71,160 


4.00 


50,400 


49,990 


66,980 


66,730 


46,670 


39,680 


61,470 


53.310 


9.00 


41,980 


43,050 


59,010 


59,460 


41,990 


47.830 


56,140 


59.480 



Erratic Results — Test Bars 



301 



24 inch centers. . They were cast from two patterns in one mould and 
made in the same kind of sand as the main casting. The flask was 
incUned about 30 degrees. There was but one gate for the two bars with 
suitable risers. The iron for the bars was poured from a small ladle of 
iron taken as nearly as possible from the middle of the pour of the m^in 
casting. 

The breaking loads were corrected for varying dimensions of the bars 

by the formula W = , where b and d are the actual dimensions, 

W the actual breaking load and W the corrected load of weight. These 
results are used throughout this paper. The deflections were not 
corrected. 

The tensile bars, 1% inches by 6 inches, were cast upright in the same 
mould as the main castings, within 3 or 4 inches thereof, and connected 
by an upper and lower gate. The tensile bars were turned to i i/i inches 
in diameter and threaded, and the middle portion reduced to 1.129 inches 
in diameter which is equal to i square inch area. Table I gives the 
results of the chemical analysis of the several bars tested. 

Table I 







s 


1 






i 


1 


3 
•a 




is 

1^ t 


CO u 


1" 






1 





a . 


§ 

^ 


fin 


03 


S 






0) 


Nov. 21, 


1907.... 


3.580 


2.830 


.75 


• 79 


.485 


.081 


1.59 


24.900 


2440 


.49 


Nov. 26, 


1907.... 


3.396 


2.736 


.66 


.38 


.459 


.124 


1. 91 


22.000 


2075 


.40 



From Aug. 5, 1907 to April 4, 1908 there were made 67 single tensile 
bars, and the same nurnber of pairs of transverse bars; and the average 
of the latter was used in this record. From April 4 to Dec. 19, 1908, there 
were made 91 pairs of tensile bars and an equal number of transverse 
bars and each piece of the pair is recorded instead of the average. 

Of these 249 tensile bars and their corresponding transverse bars, 32 
sets — 26 flat and 6 round — were rejected for defects due to blow-holes 
and four tensile bars were too hard to bear threading, but the companion 
pieces were used in this record. 

Of the 217 specimens here recorded, 42 were designated as abnormal; 
that is, the ratio between the tensile and the transverse bars was either 
considerably greater or smaller than the average. 



302 



Test Bars 



By referring to Table II it will be seen that of the 175 specimens of 
cast iron running from 20,000 to 30,000 pounds tensile strength, the 
ratio of tensile to breaking loads is practically 10 to i and the deflection 

0.45." 

Table II 



Number of 
specimens 


Transverse 


Tensile 


Deflection 


Ratio of tensile to 
transverse 


29 
36 
SI 
43 
16 


2065 
2289 
2523 
2756 
2894 


21,630 
22,940 
24,880 
26,500 
28,460 
23,732 


Inch 
.43 
.45 
.47 
• 49 
.49 


10.47 
10.02 
9.86 
9.61 
9-83 
9- 96 




175 


Average 2383 




45 





Comparison of Test Bars 

Table III gives 25 abnormal cases where this average ratio is as high as 

12.56 to I with a deflection of 0.43 inch, also 17 abnormal cases where 

this average ratio is as low as 7.91 to i, with a deflection of 0.44 inch; 

and yet the average of both normal and abnormal bars was again very 

nearly lo to i. 

Table III 

Ahove ratio 10 to i 



Number of 




Tensile 


Deflection 


Ratio of tensile to 


specimens 








transverse 








In. 






10 


2088 


27,143 


.41 


12.95 




10 


2294 


28,530 


.43 


12.44 




4 


2436 


29,600 


.49 


12.15 




I 


2890 


34,000 


.45 


11.76 




25 


Average 2258 


28,36s 


.43 


12.56 








Below 10 / 


I 




I 


2105 


17,600 


.50 


8.36 




4 


2359 


18,825 


.41 


7.98 




7 


2487 


18,814 


.43 


7.57 




3 


2656 


21,230 


.45 


8.00 




2 


2969 


24,500 


.47 


8.2s 




17 


2521 


19,954 


.44 


7.91 





Breaking loads, presumably alike, varied in pairs of transverse bars 
and also in pairs of tensile bars as follows: 



Comparison of Test Bars 



303 



Out of 65 pairs of flat or transverse bars, 14 or 22 per cent, average 
variation 18 per cent; 17 or 26 per cent, average variation 5.4 per cent; 
34 or 52 per cent, average variation less than 2 per cent. 

Out of 65 pairs of round or tensile bars 22 or 34 per cent, average 
variation 15 per cent; 20 or 31 per cent, average variation 5.5 per cent; 
23 or 35 per cent, average variation less than 2 per cent. 

61 other pairs of flat bars which had only one companion tensile bar 
varied in about the same ratios. 

Two special flat bars and two special roimd bars, cast in one mould, one 
gate and at one pour varied as follows: 

Two flat bars 12 per cent; two round bars 7 per cent. 

In order to get some more definite information on these variations, if 
possible, I had a pair of transverse and a pair of tensile bars made and 
cast in the same mould and while the average was again nearly 10 to i as 
shown in Table III, the same type of bars again varied 12 and 7 per cent 
respectively. 

Table IV 

Comparison of Cast-iron Test Bars. Special. Two Sets Cast in 

Same Mould at Same Time 



Number of 
specimens 


Transverse 


Tensile 


Deflection 


Ratio of tensile to 
transverse 


I 

I 

2 

217 


2350 
2100 

Average 2225 
All averages 2380 


23,000 
21,470 

22,235 
23,970 


Inch 
.50 
• 45 

.47 
.45 


9-79 
10.21 

10.04 
10.07 


I 
I 
I 
I 



I have no satisfactory explanation for the great variation of these test 
bars and we can only accept the fact that mathematical uniformity in 
strength of cast-iron bars is not found in the present state of the art. 

To any one questioning the results, I can only say from my own 
knowledge of the circumstances, that the personal equation did not enter 
into them. 

Careful observation of broken bars did not show that the so-called 
"skin of the metal" was of any appreciable thickness and the metal was 
remarkably homogeneous throughout. 

The tensile bars being turned, the skin, if there was any, of course 
disappeared. 

It is my opinion that the skin adds practically nothing to the strength 
in either transverse or tensile bars; other causes, though obscure, produc- 
ing far greater deviations." 



304 Test Bars 

Casting Defects 

Although many castings were condemned for physical defects not a 
single case of cold-shut was observed. 

In one instance of defect, he says: "To remove all doubt that the test 
bars were truly representative of the iron in the main casting, two tensile 
bars were cut out of a large flange which had been at the bottom of the 
mould. These, from the most favored part of the casting, as v/ill be seen, 
stood but about 17,350 pounds; 90 per cent of that revealed by the test 
bars. In this case there was a remarkable agreement between this pair 
of test bars. 

It may be interesting to apply these results to the formula for the 

strength of cast-iron beams subjected to similar stress. 

T, PI 
The formula commonly used isR= ^-^-7, , where R is called the modulus 

of rupture, or stress per square inch of extreme fibre, 

P = load at center, 
I = length between supports in inches, 
b and d = breadth and depth respectively in inches. 

Make the proper substitutions and we have R = 42,840 pounds. 
This is not the correct figure, however, for the extreme fibre stress. We 
know this cannot exceed the tensile strength which we have found to be 
23,732 pounds. 

I think it is better to use D. K. Clarke's formula given on page 507 of 

WL 

his " Engine Tables." S = r^r , where 5= extreme fibre stress or 

I. 155 bd^ 

tensile strength. If we use the tensile strength found in these tests as 
23,732 pounds, the breaking load W would become 2284 pounds; the 
actual breaking load being 2383 pounds. As this is within 4.3 per cent 
of the average found in these tests, this formula, using the tensile strength 
for the extreme fibre stress, seems to me to be more intelligible and dis- 
penses with the "coefficient of rupture." 



Circular Test Bars 

Since the foregoing was written I have had the opportunity to ob- 
serve two circular test bars, nominally iH inch diameter by 15 inches 
long, with 12-inch centers. These bars were cast from two separate 
patterns in one vertical dry sand mould, and poured from a small 
hand ladle, first one and then the other, with the result shown in 
Table V. 



Circular Test Bars 305 

Table V. — Circular Test Bars in Vertical Dry Sand Moulds 



Bar mark 


Transverse 


Tensile 


Deflection 


Value W by 
formula 


Original 
diameter 


H 


3344 

3344 

3026 

2 


23,070 

23,754 

24,670 

3 


.15 
•IS 
.12 
4 


2948 

3036 

3153 

5 


1.305 


H 


1.305 


X 


1.300 


/ 


6 







The tensile bars were taken from the bottom ends of the broken test 
bars, but I do not know whether H ox X was poured first. 

The first tensile bar H had a small air-hole, which being allowed for, 
added 7 per cent to its tensile strength, and this is also given in the table. 
A second bar was then turned up from the immediate joining piece with 
the result recorded in the table first. The turned bars were 0.937 inch 
diameter. 

Column six gives the original diameter. Column two was found by 
reducing the actual breaking loads in the ratio of the cubes of the diam- 
eters, and column three was reduced to the square inch area. Why the 
transverse breaking loads should vary 10 per cent and the tensile bars 
4 to 7 per cent the opposite way, a total variation of 14 to 17 per cent, I 
leave to the reflection of the reader. If we apply Clarke's formula for 

the breaking weight for circular bars, W = - — - — -, , we find the 

values given in column five. 

While the blow-holes seem to be more frequent in flat transverse bars 
than in round attached tensile bars, the latter seem liable to a greater 
abnormal hardness, for which I have no explanation. 

Some indication of the toughness of cast iron may be seen in its deflec- 
tion, which is not revealed in a direct pull. I would, therefore, be 
satisfied with two or three transverse test bars 2 in. by i in. by 24 in. 
centers, and a deflection record poured as near as may be from the middle 
of the pour of the main casting as giving a fair indication of the iron 
in the main casting, but mathematical exactness cannot be looked for as 
yet. 

If we wish to know approximately the corresponding tensile strength 
of the iron, we can multiply the breaking load of the 2 in. by i in. by 24 
in. flat bar by 10. 

If the test bar is iM inch diameter by 12-inch centers its breaking 
load should be multiplied by 8 to obtain the approximate tensile 
strength. 



3o6 



Test Bars 



The general rule seems to be, that where both flat bars agree in break- 
ing loads, the tensile strength is lo to i of the breaking load, but where 
they differ the lo to i ratio does not hold. A better practice, therefore, 
might be to cast three round transverse bars and accept the two that 
agree, if each is round, as a fair sample of the iron, dispensing with the 
tensile bars. This concession to the manufacturer, I believe, v/ould 
entail not only no loss to the city's interests, but a positive gain. 

EFFECT OF STRUCTURE OF CAST IRON UPON ITS 
PHYSICAL PROPERTIES 

Microscopic Evidence of the Reason why Irons of 

Similar Chemical Composition have Different 

Relative Strengths 

BY 

F. J. Cook and G. Hailstone 

" During daily foundry practice, with work made from mixtures of iron 
that have the same chemical composition and where tests are frequently 
taken, it is often found that widely different physical results are obtained. 
Instances of this have been brought to the notice of this association 
. . . but in neither case was an explanation of the phenomena given. 
Attempts have been made to give a satisfactory explanation of these 
differences, but on the whole the conclusions arrived at have not been 
generally accepted. 

In the past the instances cited have generally been isolated ones, but 
a remarkable series of tests over a lengthy period has recently been met 
with by one of the authors. 





1 




r~ 












^ 










-?- v^ 


'h 






'A ^iLi^v^-5^/... 


J/k? 


J^'l^ 


^ 




;-° 


' 3jtD A^""^^^ 




^^L\- 


-^ 


\ 


Zt^ 


V ^L 


T^ 


GJ 




>. > 












V 








X-«- 






^\-/ 


A f^ru::?:^ i5^/-,^ 


^3lJ 


/ ' ,' 


-»--^ 




t^'^l 


^^^t 2^2^55 7 


S-^ ' \ 


t^Zu 


1 '-' 




7 ' I 


Ac 'n '/nTf^ i oe ;7: ^'c< rf/ o 


V 


r.- jll 


pf — 






























- 













Fig. 78. 

Fig. 78 is a diagram of tensile test results of two series of casts, each 
representing 60 consecutive days working with irons mixed to give the 



Effect of Structure of Cast Iron upon Its Physical Properties 307 

same chemical composition, but each series made up with different 
brands of pig iron. 

That the chemical analysis was identical in each case was proved by 
analyses taken from time to time which, in each instance, for all practical 
purposes came out ahke. 

The diagram shows that the highest tensile result in the A series was 
lower than the lowest result in the B series. A summary of the whole 
of the tests is shown in Table I. 



Table I. - 


- Results of 


Mechanical Tests 








Tensile 

test, tons 

per square 

inch 


Trans- 
verse test, 

cwts. 
I in. sq. 
bar, 12 in. 

center 


Trans- 
verse test, 

lbs. on 
H in. sq. 
bar, 12 in. 

centers, 

Keep's 
test 


Shrinkage 

in inches 

y2 in. sq. 

bar. 

Keep's 

test 


Hardness 


Blast 
pressure 
in ounces 


Series 


A 


B 


A 


B 


A 


B 


A 


B 


A 

68 
48 
575'^ 
60 


B 

78 
561/^ 
64H 
56 


A 

15 
10 

123/4 

44 


B 






Highest 


12.9 

8.7 
10.7 
60 


18.3 
13. 1 

15.8 
60 


28.5 
19.0 
23.1 
33 


32.25 
25.0 
29.1 
30 


5SO 
390 
466 
58 


570 

375 

450 

59 


.182 

.144 
.140 
58 


.180 
.140 
.155 
58 


16 


Average 

No test taken . . 


13H 
39 



Each tensile test bar was i inch square and transverse and hardness 
bars were cast relatively of the same size, and on the casting they were 
to represent; while the H-inch transverse bars, which were also used 
for the shrinkage test, were cast separately by Keep's method. 

The transverse bars were cast iH inch square, machined down to 
I inch square and tested on 12-inch centers. 

Referring to Table I, it will be seen that the results of the transverse 
tests on the i inch square bars also show a marked difference, as do the 
tensile tests. It will be noted, however, that the average result of the 
transverse test on the 3'^-inch square bars is slightly in favor of the series 
which gave the weakest tensile, and with the i -inch square bar opposite 
results. This point will be referred to later. 

As the method of manipulation and the chemical composition of the 
two series were the same, it was thought that a microscopical analysis 
would reveal a cause for the vast difference. For the first investigation 
a low bar of the A series, and the highest bar of the B series were ex- 
amined. The chemical analysis of the two bars was first taken as 
shown in Table II. 



3o8 Test Bars 

Table U. — Comparative Chemical Analysis of the Two Series 



Series .... 


A 


B 




Tensile test 


9.1 tons per 

square inch, 

per cent 


18.3 tons per 

square inch, 

per cent 


Total carbon 


3.250 
2.397 
.853 
1.328 
.095 
.923 
.290 


3.092 
2.289 
.903 
- I. 314 
.101 
.909 
.335 

94.149 





















Chemical Analyses 

These analyses will be seen to be practically identical, even to the 
amount of the combined and graphitic carbon. 

To insure the results being absolutely comparative, a number of 
micrographs were each taken from the same position at the center of 
the bars. Fig. 79 shows the polished, but unetched section of the low 
bar from the A series, Fig. 80 the high bar from the B series. These 
show the size of the graphite in each case, the one having it in the form 
of long flakes, the other in very small flakes. 





Fig. 79. 

Figs, 81 and 82 show the same surfaces etched with iodine and magni- 
fied 120 diameters. In the one case the large flakes of graphite are plainly 
seen in a matrix of cementite, phosphorus eutectic, pearlite and ferrite; 
while in the other, the graphitic carbon is scarcely visible and a closer 
structure is observed. Otherwise, there is nothing very remarkable to 
account for such widely different physical results. 



Chemical Analyses 



309 



The same surfaces were then treated on the lines laid down by Mr. 
Stead at the 1909 convention, to bring into prominence the phosphorus 
eutectic. Fig, 83 shows the 9.1 ton bar, and Fig. 84 the 18.3 ton bar. 
In both cases not only is the phosphorus shown but the cementite as 
well. 

In Fig. 83 the phosphorus and cementite are evenly distributed, and 
have not taken up any definite form of structure, the graphite being also 
shown intermixed with them, but in Fig. 84 a very remarkable arrange- 
ment of a net-like formation of phosphorus and cementite is shown. As 




Fig. 81. — A Series; tensile strength 
18,200 pounds per sq. inch; mag- 
. nifi cation 120 diameters. 




Fig. 83. — A Series; tensile strength 
18,200 pounds per sq. inch; mag- 
nification 30 diameters. 




Fig. 82. — B Series; tensile strength 
36,600 pounds per sq. inch; mag- 
nification 120 diameters. 




Fig. 84. — B Series; tensile strength 
36,600 pounds per sq. inch; mag- 
nification 30 diameters. 



it had been noticed with bars previously examined that those giving 
high test had also been associated with this particular net-like structure, 
we were lead to the conclusion that probably strength was associated 
with this structure independently of what the chemical composition 
might be; we, therefore, examined a series of bars made by one of the 
authors a few years ago to show the effect on strength of different rates 
of cooling. For this experiment four bars had been made in one box, 
cast from the same ladle of metal, which was ordinary No. 3 foundry- 
pig iron. 

Taken from " castings," Aug. 1909. 



310 



Test Bars 



The rate of cooling was regulated by means of cast iron chills of 
different thicknesses placed in the moulds for three of the bars, the other 
having no iron chill. The bar without the chill gave a tensile test result 
of 8.1 tons per square inch, while the bar at the other end of the series 
broke at 15.2 tons per square inch. These two bars were selected, the 
chemical analyses of which are given in Table III. 

Table III. — Analysis of Medium Bar 



Tensile strength 



Total carbon 

Graphitic carbon . 
Combined carbon 

Silicon 

Sulphur 

Phosphorus 

Manganese 

Iron by difference 



13.9 per cent 



.272 
.740 
.532 
.307 
.III 
.948 
.330 



94.032 



Chilled and Unchilled Bars 

These results are identical, and as there is practically no combined 
carbon present, there must be an absence of cementite. The bars are 
also totally different in chemical composition from those previously 
examined. 

Figs. 85 and 86 show unetched sections from the two bars, with the 
difference in the formation of the graphite as previously pointed out in 





Fig. 8s. 



Fig. 86. 



connection with the other bars; that is, elongated flakes of graphite in 
the unchilled bar, and finely divided graphite in that of the chilled 



Figs. 87 and 88 show the formation of the phosphorus eutectic in the 
case of the weak bar to be broken up and having no distinct pattern, 
while in the case of the strong bar there is clearly shown that net-like 



Chilled and Unchilled Bars 



311 



formation which was the distinguishing feature of the strong bar from 
the B series, but with this difference, that the structure was rather 
smaller. 

As there is no cementite present in this specimen, it is proof that the 
particular formation is not dependent upon cementite. 





Fig. 87. 



Fig. 88. 



There was next examined another bar from B series. This had a 
tensile strength about half way between the two bars previously selected, 
and had given a tensile test result of 13.9 tons per square inch. The 
analysis of this bar is shown in Table III. This showed that while the 
total carbon and other elements were practically the same as the two 
bars previously taken, the graphitic carbon was higher by 0.35 per cent, 
and the combined carbon lower by 0.35 per cent. This was probably 
due to the fact that this bar had been cast on a much larger casting than 
the previous two. 

The size of the graphite in this bar is illustrated by an unetched 
section in Fig. 89 which shows that although it is smaller than that shown 
in Fig. 79 of the 9.1 ton bar, it is larger and more elongated than that 
contained in the 18.3 bar, Fig. 80. 





Fig. 89. 



Fig. 90. 



The phosphorus eutectic which is shown in Fig. 90 is the same net-like 
formation as associated with the previous strong bars, though rather less 
clearly defined and appears to be getting into the transition stage between 
the two. 



312 Test Bars 

The foregoing results, we think, have been sufl5cient to show that in 
each case, physical properties have been associated with this net-like 
formation of the phosphorus, also that the graphite, when in the elongated 
form, appears to split up phosphorus eutectic and prevent this formation, 
as clearly shown in Fig. 83. The question of the tendency of the graphite 
to take either an elongated or finely divided form, we think, is more a 
question of the way in which the pig iron has been made than of its 
subsequent treatment in the foundry. The statement of Mr. Pilkington 
in this respect is very interesting: "Furnace men have always been 
conversant with the fact that the temperature at which" pig iron leaves 
the tapping hole of the furnace has a powerful effect on its physical 
characteristics. The temperature of a large modern blast furnace is 
very much higher and the metal, therefore, takes very much longer to 
cool than that which leaves the tapping hole of the smaller furnaces. 

Pig iron from the extreme types could be made practically in a 
different manner altogether, and would show very different grades, grains 
and degrees of hardness. 

On referring again to the summary of tests taken with the A and B 
series it will be seen that the results of the J-^-inch transverse bars of the 
A series, which gave weak tensile results, are slightly higher than those 
of the B series, and from this, together with the evidence of the chilled 
and unchilled bars made from low grade iron, we are of the opinion that 
no matter what their chemical compositions ma,y be, there is a rate of 
cooUng which will give high physical properties; the structure of the 
iron then being associated with the net-like formation of the phosphorus 
eutectic and the cementite when present. 

Tests reported to the International Association for Testing Materials 
show: 

-Circular bars showed greater bending and tensile strength than those 
of rectangular section. 

Test pieces taken from castings showed lower strength figures than bars 
separately cast. 

Extracts from Prof. Porter's Report 
Prof. Porter's report contains so much information of value to the 
foundryman, that extensive extracts are made from those parts relating 
to the properties and mixtures offcast iron, notwithstanding they may 
comprise much which has already been considered. 

In treating of the different forms of iron as occurring at differ- 
ent temperatures, they are designated as the "alpha," "beta" and 
"gamma." 
The "alpha" form in the ordinary iron as known in unhardened steel 



Chilled and Unchilled Bars 



313 



at ordinary temperatures, is one of the constituents of slowly cooled 
gray pig iron, and is formed below 1140° F. 

The "beta" form is that between 1440° F. and 1680° F.; it is harder 
than the "gamma." Prof. Howe suggests its identity with martensite, 
the chief constituent of hardened tool steels. It is non-magnetic and 
differs from "alpha" iron in specific heat and density. 

The "gamma" form is the stable one above 1680° F., is very hard, 
non-magnetic, and differs in specific heat and density from both the 
"alpha" and "beta." 

It is held that the "gamma" and "beta" forms may be preserved at 
ordinary temperatures by very rapid coohng, especially in the presence 
of carbon which is supposed to retard the change from one form into 
another. 

Table I. — Forms of Combination or Iron and Carbon 



Name 


Synonyms 


Physical characteristics 


Graphite 








size. No strength. 


Kish 


Free carbon . . - 


Graphite in very large flakes. 


Temper carbon 


Free carbon 


Graphite in form of very fine 






powder. 


Ferrite 


Iron 


Soft, very ductile, low strength. 


Cementite 


Combined carbon. Iron car- 


Very hard and brittle, high static 




bide, FeC. 


strength, no ductility. 


Austenite 


Solution carbon in "gam»la" 


Slightly softer than martensite. 




iron. 


Also weaker and more brittle. 


Martensite 


Solution carbon in "beta" 


Hard, but less brittle than ce- 




iron. Transition product 


mentite. Chief constituent of 




austenite to pearlite. 


hardened tool steels. 


Troostite 


Transition product marten- 


Softer than martensite, less 




site to sorbite. 


brittle and more ductile. 


Sorbite 


Transition product. Troost- 


Softer than troostite and more 




ite to pearlite. 


ductile. Strongest form. 


Pearlite 


An intimate mechanical mix- 


Very strong. Harder than fer- 




ture of cementite and fer- 


rite. 




rite. 





Prof. Porter classifies the more important physical properties of cast 
iron as follows: 

Static strength, indnding: Tensile strength; compressive strength; 
transverse strength; torsional strength; shearing strength. 

Dynamic strength, embracing: Resistance to repeated stress; resist- 
ance to alternating stresses; resistance to shock. 

Elastic properties, embracing: Elastic limit; resilience or elasticity; 
rigidity; toughness; malleability. 



314 Test Bars 

Hardness, embracing: Hardness of mass; ability to chill; hardness 
of chill. 

Grain structure, including: Fracture or grain size; porosity; specific 
gravity. 

Shrinkage, embracing: Shrinkage of the hquid mass; shrinkage of the 
sohd mass; stretch. 

Fluid properties, embracing: Fusibility; fluidity. 

Resistance to heat, embracing: Resistance to continued heat; resist- 
ance to alternate heating and cooling; resistance to very low temperatures. 

Electrical properties, including: Electrical conductivity; magnetic 
permeability; hysteresis. 

Miscellaneous properties, including: Resistance to various corrosive 
agencies; resistance to wear; coefficient of friction. 

Properties of the mass: Soundness, or freedom from blow-holes and 
shrinkage cavities; cleanness, or freedom from inclusions of dross, etc.; 
freedom from pin-holes and porous places; homogeneity, or lack of 
segregation; crystallization; freedom from shrinkage strains; tendency 
to peel off sand and scale. 



CHAPTER XIII 
CHEMICAL ANALYSES 

Strength 

As regards chemical composition there are nine factors which influence 
strength of cast iron: (i) Per cent graphite; (2) size of individual graphite 
flakes; (3) per cent combined carbon; (4) size of primary crystals of 
solid solution Fe-C-Si; (5) amount of dissolved oxide; (6) per cent 
phosphorus; (7) per cent sulphur; (8) per cent silicon; (9) per cent 
manganese. 

1. "Per cent graphite. — The weakening effect of graphite is due to 
its own extreme softness and weakness, and to the fact that it occurs 
in small flakes or plates and hence affords a multitude of cleavage planes 
through the metal. The size of the graphite particles is evidently 
important as well as the amount but this factor will be discussed under 
another head. 

Theoretically^ the simplest method of decreasing graphite is to lower 
the silicon, each decrease on i per cent in silicon lessening the graphite 
by 0.4s per cent, provided the total carbon remains the same. Practi- 
cally, however, the fact that all the carbon not graphite becomes combined 
is an important objection, for when we lower the silicon too much the 
resulting increase in combined carbon increases the hardness and, beyond 
a certain point, decreases the strength. The minimum permissible 
silicon will depend chiefly on the hardness allowable, 

The same objection applies to decreasing the graphite by increas- 
ing the sulphur and manganese, and in the case of sulphur there is 
also the objection that its direct effects are injurious. The rate of 
cooling is, of course, beyond the control of the foundryman in the 
majority of cases, while even if it were not, the graphite could not 
be reduced by rapid cooHng without a corresponding increase in com- 
bined carbon. 

Coming finally to the total carbon, we find here a means of reducing 
graphite without in any way affecting carbon, and hence, hardness. 
The only hmitation to this is that as total carbon and graphite are 
reduced, shrinkage is increased and the metal becomes more liable to 
oxidation, blow-holes and other defects. 

315 



3i6 Chemical Analyses 

There are three ways of reducing total carbon in castings; first, by 
the use of low carbon pig iron; second, by melting in the air furnace; 
third, by the use of steel scrap in the cupola mixture. 

In air furnace melting it is easy to reduce total carbon to almost any 
figure within reason. 2.75 per cent is commonly obtained in melting for 
malleable castings. Of course the silicon is also burnt out during this 
process, but were it desired, this could be readily replaced by suitable 
additions of ferrosilicon. From the standpoint of quality the air 
furnace is certainly the ideal method of melting, and hence, we find that 
many lines of castings which must be of particularly high quality are 
invariably made from air furnace metal. 

The addition of steel scrap to the cupola has now become common 
practice, the product obtained being known as semi-steel and differing 
chemically from ordinary cast iron only in being somewhat lower in 
total carbon and graphite. Physically the metal so made is characterized 
by greater strength and total shrinkage, hardness remaining about the 
same. ..." 

The chief points to be watched in melting steel scrap in the cupola 
mixture are as follows: 

" Trouble with blow-holes. — This is due to the fact that semi-steel being 
lower in carbon oxidizes more readily than cast iron. The trouble may 
usually be overcome by correct cupola practice and the use of ferro- 
manganese or other deoxidizers in the ladle. Owing to the higher 
melting point of semi-steel mixtures, ferromanganese is much more 
efficient as a deoxidizer here than in the case of cast iron. . . . 

High shrinkage. — This is due to the decrease in graphite and is 
hence inevitable. On work where this is an important factor a proper 
balance must be struck between shrinkage and strength. . . . 

Imperfect mixture of steel and iron resulting in irregular quality of 
casting, hard spots, etc. — This results from the higher melting point of 
steel and consequent difficulty of getting perfect solution in the cast 
iron. It may be largely overcome by careful attention to the charging 
of the cupola, placing the steel scrap on the coke and the iron on top of 
the steel (so that the steel will reach the melting zone first and the molten 
pig will run down over the heated steel instead of away from it as would 
happen if the order were reversed). A large receiving ladle should, of 
course, be used also. Another point to be observed is in regard to the 
size of the steel scrap. Too large scrap is difficult to melt, but, on the 
other hand, very small scrap is also objectionable as being an abundant 
source of hard spots in the castings. Apparently very small pieces of 
steel are Uable to be washed down through the coke bed and out of the 
cupola spout without being completely melted. 



Strength 317 

Regarding the amount of steel scrap to use, it has been found by trial 
that the best results are obtainable with about 25 per cent. Increase to 
S3H per cent caused a slight falling ofif in strength. Probably these 
figures would not hold for every condition of practice, but, in general, 
20 to 30 per cent steel is a suflQcient amount to give the maximum 
results. 

2. Size of graphite flakes. — The size of the graphite flakes is prob- 
ably the most important factor of all those which influence strength, and 
is the one which most frequently upsets our calculations as to the rela- 
tion between chemical composition and strength. . . . Recently, how- 
ever, Messrs. F. J. Cook and G. Hailstone have brought out in a striking 
manner the great difference in irons in this respect. They give data 
showing that of two mixtures practically identical in composition the 
one was invariably much lower in strength (usually about one-half) 
than the other, this being the case for a great many heats extending over 
a long period of time." 

Analyses and tests are given as typical of the series. 

"Messrs. Cook and Hailstone have investigated and compared the 
micro-structure of the strong and weak bars and record two interesting 
facts: First, that the graphite flakes are invariably much larger in the 
weak bars; second, that when the polished specimens are treated so as 
to bring out the phosphide eutectic this eutectic is seen to be arranged 
in the customary heterogeneous mamner in the weak bars but in a dis- 
tinct meshwork structure in the strong iron. 

These authors draw the conclusion that it is this meshwork structure 
which gives great strength to cast iron, but with this conclusion the 
writer cannot entirely agree. It seems more probable that the increase 
in strength is caused by the fine state of division of the graphite and that 
the same influences which have caused this have also caused the meshwork 
structure. 

We may get some idea of the quantitative relationship between 
strength and size of graphite by considering the relative strength of 
malleable cast iron and a very open gray cast iron representing the 
smallest and largest graphite respectively. Malleable cast iron has a 
tensile strength of 40,000 pounds and upwards per square inch; open 
gray iron about 20,000 pounds per square inch. Apparently, then, the 
increase in the size of the graphite has caused a loss of at least 20,000 
pounds in tensile strength. 

It is one thing to find that to get strong iron we must have the 
graphite in finely divided state and another and much more difficult 
matter to formulate rules whereby we may secure this desired 
condition. . . .' 



3i8 Chemical Analyses 

The factors which influence the size of the graphite flakes in cast 
iron are as follows : 

A. Factors which certainly exert an influence. 

a. Rate of cooling. 

b. Pouring temperature. 

B. Factors which may possibly exert an influence. 

c. Time which iron has remained in the molten state, 

d. Presence of dissolved oxide. ' - 

e. Presence of steel scrap in the mixture. 
/. Mixture of different brands. 

g. Nature of ore from which iron is made and treatment in the 

blast furnace. 
h. Per cent metalloids. 

a. The influence of rate of cooling is undoubted, and an example 
showing its effect on strength and fitructure is given by Cook and Hail- 
stone. We have to distinguish here, however, between the rates of 
cooHng through different ranges of temperature. Evidently the graphite 
which is separated within the semi-hquid iron will have a much better 
chance to grow large crystals owing to the greater mobihty of the medium 
in which it is formed, while that graphite formed within the soUd metal 
will necessarily be in small particles. Hence, we see that it is the rate 
of cooling through the soHdificatioti range 2200° to 2000° F., which is 
of prime importance, and if we can check the formation of graphite 
through this range and then allow it to form in the solid metal at lower 
temperatures we will have all the conditions for both the soft and strong 
iron. This is the principle of Custer's process of casting in permanent 
moulds and the making of malleable castings is based on the same theory." 

b. The pouring temperature also undoubtedly exerts an influence 
on the size of the graphite flakes, and hence, on the strength. ..." 

Longmuir finds that iron poured at a medium temperature is stronger 
than when poured either very hot or very cold. Longmuir' s experi- 
ments, by the way, are the only ones in which a pyrometer was used and 
the temperatures of pouring measured in degrees. . . . For this 
reason we may place the greatest faith in Longmuir's results. 

It is probable that the pouring temperature affects the size of the 
graphite flakes indirectly through changing the rate of cooling through 
the solidification range. On this assumption the best results should be 
obtained from metal poured at as low a temperature as will suffice to 
give sound castings. 

c. Time which iron has remained in the molten state. This might 
conceivably have an effect in the case of cast iron high in total carbon, 



Strength 319 

since graphite separating in the hquid metal would remain in the metal 
if poured at once, and this graphite is in the form of large flakes known 
as kish. 

d. Presence of dissolved oxide. — There is no direct proof that this 
affects the size of the graphite flakes. However, it is well known that 
addition of deoxidizing agents almost invariably improves the strength 
and it is barely possible that a portion of this may be due to change in 
the size of the graphite. 

e. Presence of steel scrap in the mixture. — Although no exact data 
are at hand it is the common impression that the addition of steel scrap 
'closes the grain,' which is equivalent to saying that it reduces the size 
of the graphite. . . . 

/. Mixture of irons. — It is firmly believed by many foundrymen 
of the old school that a mixture of brands gives better results than a 
single brand of the same chemical composition as the average of the 
mixture. ... 

g. Cook and Hailstone believe that the difference in strength of the 
two mixtures quoted by them is due to some inherent quality of the pig 
iron derived from the ores used or their nianner of treatment in the blast 
furnace. This inherent quahty may have some connection with the 
presence of oxygen or nitrogen in the metal. . . ." 

h. Per cent metalloids. — This, we know, has a certain effect. For 
example, high silicon is likely to cause larger graphite as well as more 
of it. Phosphorus should, theoretically, cause larger graphite since it 
prolongs the solidification period in which large flakes are free to separate. 
. . . Sulphur and manganese . . . close the grain, and probably 
diminish the size of the graphite, as well as its amount. 

3. Per cent combined carbon. — According to Professor Howe the 
properties of cast iron are the properties of the metallic matrix modified 
by the presence of the graphite, but since this metallic matrix may be 
considered as a steel of carbon content equal to the combined carbon of 
the cast iron, we can predict accurately the effects of combined carbon 
by the use of the data on steel. 

In the case of steel it is found that the strength increases regularly 
with the carbon up to about 0.9 per cent, then remains nearly stationary 
up to about 1.2 per cent, above which it falls off slowly. 

In the case of cast iron the strength is dependent upon so many 
factors besides combined carbon that it is almost impossible to determine 
by direct experiment the percentage of combined carbon giving the 
maximum strength. All indications, however, are that the highest 
strength is obtained with somewhere between 0.7 per cent and i per cent 
combined carbon which is in sufficiently close accord with the corre- 



320 Chemical Analyses 

spending value for steel. We may, therefore, state tentatively that the 
maximum strength is obtained with 0.9 per cent carbon, all other factors 
remaining constant. 

This appb'es only to tensile strength (and approximately to transverse). 
For compressive strength a somewhat higher value, probably about 1.5 
per cent combined carbon, would be found to give better results. 

4. Size of primary crystals of solid solution Fe-C-Si. — There is 
absolutely no data as to the effect of this factor on the strength of cast 
iron and it is only from analogy with steel that we give it a place in the 
list of actors influencing strength. ..." 

5. Effect of dissolved oxide. — . . . It is probably a much more 
important factor than is generally supposed, but there is absolutely no 
data on which to base a quantitative estimate of its effect." 

To reduce oxide in cast iron to the minimum, the following points 
may be observed : 

First, get the best brands of pig iron. It is probable that pig made 
with charcoal fuel contains less oxygen than that made with coke fuel. 
Cold blast pig is better than hot blast. Pig iron made from easily 
reducible brown or carbonate ores is lower in oxygen than the pig made 
from red hematite or magnetic ores, while iron made from mill cinder 
should never he used in foundries where strength is a prime consideration. 
Moreover, a pig iron high in manganese is apt to be comparatively free 
from oxide because of the deoxidizing power of manganese at the high 
temperature of the blast furnace. It is noteworthy as confirming these 
observations that most brands of iron which have achieved a reputation 
for strength are high in manganese and many of them are charcoal irons. 
The Muirkirk and Salisbury brands which have been known for years 
as among the strongest irons made in this coimtry answer to every 
one of these conditions. They are made from readily reducible ores 
using cold blast and charcoal fuel and contain from i to 2 per cent 
manganese." 

Second, avoid oxidizing conditions in the cupola, particularly high- 
blast pressures and wrong methods of charging. Dr. Moldenke's 
system of using small charges is to be highly recommended in this 
connection." 

Third, deoxidizing agents may be used, added either to the cupola 
or to the metal in the ladle. Of the commercially available deoxidizers, 
ferrotitanium, ferrosihcon and ferromanganese are, perhaps, the most 
successful, all things considered. Titanium thermite is also extremely 
valuable in this connection. . . . " 

6. Per cent phosphorus. — Phosphorus lessens both the dynamic and 
static strength, but the former more than the latter. It weakens be- 



' Strength 321 

cause it forms with iron a hard and brittle compound which has but 
little resistance to shock. The weakness produced is in nearly direct 
proportion to the amount of this compound present. The effects of 
phosphorus on strength do not become marked until upward of i per 
cent is present, but for great strength and particularly strength to shock 
it should be much lower. Ordinary strong irons may have up to 0.75 
per cent, while iron which is to withstand shock should not exceed 0.50 
per cent and is better even lower. . . ." 

7. Per cent sulphur. — The action of sulphur in decreasing the strength 
of iron is explained in Chap. IX, page 261, and it is also explained 
there why it is so much less harmful in the presence of manganese. 
Many tests have been made showing that sulphur has no marked effect 
on strength and many foundrymen will use sulphur to harden iron and 
close the grain. It is true that an indirect strengthening effect can be 
obtained through the use of sulphur in some cases, i.e., if too soft an 
iron is being used the strength will be increased by the addition of any 
element which will lessen the graphite, but the hardening is usually better 
obtained through decrease in silicon than through increase in sulphur. 
While increased sulphur may not always show in decreased strength of 
test bars, yet it is a frequent source of blow-holes, dirty iron and various 
defects caused by high shrinkage, hence, it often causes an indirect 
weakness in the iron. 

8-9. Per cent silicon and manganese. — These elements act chiefly in 
an indirect manner and because of their effects on the condition of the 
carbon; their direct influence in the strength of the metallic matrix is 
unimportant. From analogy with steel it is probable that sihcon in 
amounts of over i per cent causes weakness and brittleness in the metal. 
Similarly, manganese has probably a weakening effect due to its direct 
action when present in amounts of more than 1.5 per cent. 

The preceding discussion is summarized in the following practical 
rules for making strong castings: 

Use strong brands of iron. . . . Charcoal irons if cost wiU permit; 

irons made from easily reducible ores; irons high in manganese. 
Avoid oxidation in melting. Look carefully after the details of 

cupola practice; avoid oxidized scrap; use deoxidizing agents in 

ladle if practicable. . . . 
Keep the silicon down as low as possible and still have the necessary 

softness. About 1.50 per cent will be right for the ordinary run 

of medium castings; higher for small castings and lower for 

heavy ones. With low total carbon high sihcon has less effect. 
Keep the phosphorus low, especially when sulphur is high. 0.50 

per cent or under is best. 



322 Chemical Analyses 

Keep the sulphur low, especially if phosphorus is high. Under 

o.io per cent is all right for most castings." 
Keep manganese high, i per cent for large castings, 0.7 per cent 

for medium, 0.5 per cent for small castings. 
Use from 10 to 25 per cent steel scrap in the mixture. 
Me. Keep recommends using 10 per cent cast iron borings charged 

in wooden boxes. He states that this is very effective in closing 

the grain and strengthening the castings. 

For iron which is required to have the greatest possible resistance 
to shock, the points to be especially observed are as follows: 

Keep the phosphorus as low as practicable, still having the necessary 
fluidity. It should best be below 0.30 per cent. 

Keep the sulphur as low as possible. 

If practicable add vanadium or titanium to the ladle either in the 
form of ferroalloy or as thermite. ... 

Elastic Properties 

Of the elastic properties of metals, only toughness and its opposite, 
brittleness, and elasticity and its opposite, rigidity, are ordinarily con- 
sidered in cast iron. 

Toughness is defined as resistance to breaking after the elastic limit 
is passed. 

Elasticity is the amount of yield under any stress up to the elastic limit. 

It is unusual for these properties to be determined separately in cast 
iron, but their sum is given by the deflection which is determined in 
transverse testing. It is probably true that they nearly always vary- 
together, and, hence, that deflection is a fairly good measure of either 
one as well as both. 

Toughness is practically always a desirable quality in cast iron, but 
the same is not true of elasticity since in many machines great rigidity 
is a prime requisite. 

The factors influencing toughness and elasticity are about the same 
as those influencing strength, i.e., the chemical composition, presence of 
oxide and size of graphite. ... In general, to get a tough elastic 
iron we should keep sulphur, phosphorus and combined carbon low; 
manganese, no higher than is necessary to take care of the sulphur; 
graphite and silicon, the less the better, providing that the combined 
carbon is not increased; and finally, use metal of good quahty, melted 
carefully so as to be free from oxide. 

In ordinary gray iron castings it is not practicable to attempt to 
control the graphite, since the combined carbon needs first attention and 



Elastic Properties 



323 



the graphite will necessarily be the difference between total carbon and 
combined carbon. The silicon also must be adjusted with a view to 
regulating the combined carbon. Practical rules for getting the maxi- 
mum toughness and elasticity will then be about as follows: 

Sihcon, 1.5 to 2.0 per cent for castings of average thickness, more or 
less for very Hght and very heavy castings respectively. 

Sulphur as low as practicable, best under 0.08 per cent. 

Phosphorus as low as practicable considering the necessity for 
fluidity. Best under 0.50 per cent. 

Manganese from three to five times the sulphur. 

Use good irons and good cupola practice to insure freedom from 
dissolved oxide. . . . 

"In case steel scrap can be used, i.e., semi-steel made, the toughness 
may be considerably increased through decrease in the amount of graphite 
and in the size of the grain. The other elements may remain about as 
before except that it may be necessary to run the manganese a Uttle 
higher to counteract the greater tendency of the semi-steel to become 
oxidized. 

As previously noted, rigidity is desirable in some cases. This is the 
converse of elasticity and may be obtained by the direct opposite of the 
rules given for obtaining elasticity. However, to get rigidity with the 
least sacrifice of strength and toughness it is desirable to use manganese 
and combined carbon rather -than to increase phosphorus and sulphur. 
That is, we would lower silicon as much as necessity for softness will 
allow and raise manganese to about i per cent (or less in very light work). 
It should be noted that manganese is particularly efficient in increasing 
rigidity since it accomplishes this end with comparatively little sacrifice 
of strength and toughness. 

A few examples of very tough and elastic iron are as follows: 



No. 


Silicon 


Sulphur 


Phos- 
phorus 


Manga- 
nese 


Com- 
bined 
carbon 


Graphite 
carbon 


Total 
carbon 


I 


2.5c^2.75 

.80 

2.45 

1. 18 

2.36 




050 




30 


.43 
.30 

.24 


.87 
1,08 


2.34 
2.15 


3.21 


3 

4 
5 




092 
084 
064 




063 

27 

33 


3.23 



No. I represents iron which in thin sections can be punched and bent. 
No. 2 is an analysis of a gray cast iron which is exceedingly malleable. 
Nos. 3, 4 and 5 are gray irons sho^Adng deflections for the transverse test 
bars rather higher than usual. 



324 Chemical Analyses 

Hardness 

... It is generally stated that hardness in cast iron is due chiefly 
to the presence of combined carbon and is only indirectly or to a less 
extent caused by other elements. The writer believes that this is not 
altogether true and that there is another factor causing hardness which 
has not heretofore been generally considered in the case of cast iron." 

It is well known that when steel is hardened by quenching from a 
temperature above its critical point its carbon is not in the combined 
state but rather in a form known as hardening or solution carbon, while 
the iron is retained in the ' gamma ' allotropic form. It is the behef of 
the present writer that the same is true of cast iron and that many cases 
of hardness are to be explained in this way. For example, Keep de- 
scribes a sample of cast iron which was too hard to drill and yet contained 
only 0.60 per cent combined carbon, and many analyses are on record 
of irons which have been quenched from comparatively low temperatures 
and are almost glass hard in spite of the fact that the combined carbons 
are under i per cent. I think it probable that the hardness of high 
manganese irons is due chiefly to this same cause since manganese is 
known to favor the retention of ' gamma ' iron. 

Granting for the present the truth of this theory, the presence of the 
'gamma' or hard form of iron is controlled by the rate of cooHng and the 
percentages of metalloids present; so that for aU practical purposes we 
can say that there are six factors which influence hardness, i.e., the rate 
and manner of cooling, the combined carbon, silicon, sulphur, man- 
ganese and phosphorus. The first two of these are of the greatest 
importance and we will then take up in reverse order, leaving the most 
important till the last. 

Phosphorus has a shght hardening effect in large quantities but in 
amoxmts less than i per cent its effects are nearly imperceptible, and it 
does not become important until the amount exceeds commercial Hmits, 
or, say, 1.5 per cent. We may, therefore, usually neglect the effects of 
phosphorus in considering hardness. 

Manganese, although usually regarded as a hardening agent may 
sometimes soften iron. This anomalous resiilt is explained by the action 
of manganese on sulphur. If the iron is high in sulphur and low in 
manganese the first additions of manganese will unite with the sulphur 
forming the comparatively inert manganese sulphide and thus softening 
the iron. If, however, the manganese be increased beyond the amount 
necessary to care for the sulphur, increased hardness will result. 

... A pig iron containing 3 per cent manganese may have a 
beautiful open gray fracture and yet be so hard as to be drilled pnly 



Hardness 325 

with great difficulty. In addition, the presence of manganese sometimes 
produces a peculiar kind of gritty hardness, the iron acting as if contain- 
ing small hard grains. With regard to the amount of manganese re- 
quired to produce hardness it will be evident that this depends largely 
on the per cent of sulphur present and also on the rate of cooHng. In 
general, heavy castings will stand up to i per cent of manganese without 
noticeable increase of hardness, medium castings about 0.75 per cent 
and Ught castings 0.50 per cent. 

Sulphur is an exceedingly energetic hardening agent acting, however, 
chiefly through the carbon. That is, sulphur has a strong tendency to 

keep the carbon in combined form and in that way to harden 

Each o.oi per cent sulphur will increase the combined carbon by about 
0.045 PSJ" cent, other things being equal. It must be remembered, how- 
ever, that this applies only to sulphur in the form of iron sulphide, and 
that in the form of manganese sulphide, i.e., in the presence of about 
three times its weight of manganese, it acts much less energetically. 

Sulphur also has a direct action in hardening, iron sulphide and 
manganese sulphide being quite hard substances. Usually this action 
is imperceptible, but occasionally one meets with hard spots which are 
due to the segregation of these sulphides. 

SiHcon is generally known as a softening agent and, within reasonable 
limits, has this effect due to its action in decreasing the combined carbon. 
The direct effect of silicon, however, is to harden since it forms with iron 
a compound which is harder than the iron itself. 

When silicon is added to cast iron its first effect, as before stated, is 
to decrease the combined carbon. This, it does, at the rate of about 
0.45 per cent for each per cent of silicon added. Actually the rate of 
decrease is more rapid than this, and, in consequence, by the time we 
have from 2 to 3 per cent silicon present (depending on the rate of cooHng) 
we have practically all the combined carbon precipitated out as graphite 
and, hence, there is no further possibihty of softening in this way. Now; 
any increase in silicon only increases the amount of the hard iron-silicon 
alloy, there is no more combined carbon to be decreased, and, hence, the 
hardness will now be increased again. In other words, it is possible to 
have too much of a good thing, the good thing in this case being silicon. 

The actual percentage of sihcon which is necessary to secure any 
given degree of softness will depend upon the size of the casting, the 
nature of the mold and the amount of sulphur and manganese present. 
It is, therefore, impossible to give definite silicon standards unless each 
of these factors is known. . . . 

Combined carbon (or solution carbon) is the chief hardening agent 
of cast iron, and, under ordinary conditions, the hardness of the metal 



326 Chemical Analyses 

will be closely proportional to the percentage present. Of such relative 
unimportance are the effects of the other elements that it has been found 
practicable to use the amount of combined carbon as a measure of the 
hardness of castings and as a means of predicting their behavior in the 
machine shop. ... 

"To machine easily, cast iron should not contain over 0.75 per cent 
combined carbon, i.oo per cent combined carbon gives a pretty hard 
casting and 1.50 per cent is about the upper Hmit for iron to be machined. 

The rate and manner of cooling of the casting are usually supposed 
to influence its hardness only as it affects the percentage of combined 
carbon. That it does affect the amount of combined carbon is a well- 
estabHshed fact. . . . However, we sometimes get hardness in the 
absence of any considerable amount of combined carbon. Hence, there 
must be some other factor at work, which, in the writer's opinion, is a 
solution of carbon in 'gamma' iron, the hard constituent of tool steel. 

According to this theory, combined carbon disappears in the tem- 
perature range 2200° F. to 1500° F., while 'gamma' or hard iron is not 
transformed into the ' alpha ' or soft variety until the casting has cooled 
to about 1300° F. Evidently, then, ordinary rapid cooling of castings 
from the melted state results in both high combined carbon and high 
'gamma' ;ron, and hence we have hardness due to both of these causes. 
The more rapid the cooling, the higher the combined carbon and the 
higher also the 'gamma' iron, therefore, since both vary together, the 
percentage of combined carbon is a satisfactory measure of the hardness 
produced by both factors. 

"If, now, the conditions of cooling are changed, this need no longer 
be the case. For example, suppose we cool the casting slowly from the 
molten state down to 1600° and then quench it in water. In this case 
we would get nearly all combined carbon changed to graphite diuring the 
slow cooling through the upper range, while the rapid cooling through 
1300° preserves the ' gamma ' iron solution and hence gives hardness due 
to this cause. 

Some of the peculiar things noted in connection with Custer's process 
of casting in permanent moulds are to be explained on this basis. Also, 
the much greater softness of castings which have been allowed to cool 
in sand and thereby anneal themselves over those shaken out soon after 
being poured. 

" Chilled iron is simply white iron, that is, iron in which graphite is 
absent and the carbon all in the combined or solution state. The same 
iron may be both gray and white, depending on rate of coohng and hence 
the exterior of the casting, if rapidly cooled, may be white while the 
interior which cools more slowly remains gray. Usually there is an 



Hardness 



327 



intermediate zone having a mottled structure formed through the inter- 
lacing and the gradual merging of the gray and white. A chiUing iron, 
then, is one which when rapidly cooled contains all of its carbon in the 
combined state. The factors which influence the depth and quahty 
of chill are the temperature at which the iron is poured, and the amounts 
of silicon, sulphur and phosphorus, manganese and total carbon, besides 
some of the elements which are not normally present in cast iron, but 
which are occasionally added. 

The higher the temperature at which iron is poured the deeper the 
chill, other things being equal, and it is usually considered advisable to 
pour chilled castings from hot iron. The quantitative effects of pouring 
temperature have been studied by Adamson, and while there are some 
conflicting results, it is in general indicated that in the case of the strongly 
chilling irons an increase of 50° in the pouring temperature causes an 
increase of from H to J4 inch in the depth of the chiU. 

The most important element in its effects on chill is silicon, which has 
the strongest action in precipitating graphite. For chilling iron, silicon 
should be low, but how low depends on the thickness of the casting, the 
temperature of pouring and the depth of chill desired as well as on the 
percentage of other elements in the iron. Table I gives a very approx- 
imate relationship between the percentage of silicon and depth of chill, 
other elements bei^ about normal. 



Table I. 



Approximate Relation Between Per Cent 
Silicon and Depth of Chill 



Silicon, 
per cent 


Depth of 
chill, 
inch 


Silicon, 
per cent 


Depth of 

^ chill, 

inch 


I. SO 
1.25 
1. 00 


Me 

3/16 


.75 
.50 
.40 


■ 

H 
H 

I 



Sulphur ^tends to increase the combined carbon, and, hence, the chill. 
So marked is its influence in this respect that it is sometimes added 
to cast iron to increase the depth of the chill. This,' however, is not 
usually good practice since the chill imparted by sulphur is lacking in 
toughness and strength as well as in resistance to heat strains. Scott 
cites the case of stamp shoes for mining machinery where sulphur was 
used to increase the chill. The shoes were very hard at first, but soon 
went to pieces under the repeated blows. Johnson, also, has noted the 
great difference between high and low sulphur chilled iron as regards 



328 Chemical Analyses 

ability to withstand the strains of sudden cooling without cracking. On 
the other hand, West states that the chill produced by sulphur is very 
persistent to frictional wear, and, hence, it may be inferred that sulphur 
adds to the life of castings which are subject to abrasion. It has been 
stated that the presence of a small amount of sulphur is essential in order 
to get the best results in chilled rolls. This, however, is doubtful and 
it is believed that it is only rarely that sulphur is desirable in chilled 
castings. The presence of a moderate amount of manganese in cast 
iron greatly lessens the bad effects of sulphur in chilled as well as in gray 
iron castings. 

"Phosphorus in the amounts ordinarily present in commercial cast 
iron has but slight influence on the depth of the chill but does have a 
more or less injurious effect on its strength. It is generally stated that 
high phosphorus has the effect of causing a sharp hne of demarkation 
between the gray and chilled portions of the casting. . . . It is believed 
that it is best to limit the phosphorus in chilled iron to about 0.4 per cent. 

Manganese, since it tends to increase the combined carbon, also tends 
to increase the chill; However, it must be remembered that the first 
effect of manganese is to neutralize sulphur, and, therefore, in small 
amounts it may indirectly decrease the chill. Manganese very greatly 
increases the hardness of the chill, and, to a less extent, its strength. It 
also increases the resistance of the chill to heat stjjain and whence di- 
minishes the danger of surface cracks in such castings as chilled rolls and 
car wheels. Still another effect is the promotion of a more gradual 
merging of the gray and chilled portions of the castings. Manganese 
is usually considered a desirable constituent of chilled iron and the 
amounts used vary all the way from 0.40 up to 3.0 per cent. . . . 

Of late years, semi-steel mixtures have been used to some extent for 
chilled castings, the total carbon being considerably lower than in the 
ordinary mixture. The effect of low total carbon is to give a deep and 
comparatively soft chill as compared with the shallow, hard chill obtained 
with high total carbon. 

"It has been proposed to use nickel as a means of controlling chill, 
this element having an effect somewhat similar to silicon. Hence, by 
starting with a strong chilhng iron and adding nickel, the depth of the 
chill would be lessened in some ratio to the amount of nickel added. 
Since the same results may be obtained by the use of less expensive 
sihcon it is difficult to see any advantage in adding nickel. 

The quality of chilled iron may be very greatly improved by the 
addition of small amounts of titanium or vanadium. The beneficial 
effects of these elements are probably due chiefly to their deoxidizing 
power. . . . 



Shrinkage 329 

Grain Structure 

"The fracture or grain size and the porosity are closely related and 
are both dependent primarily on the size of the graphite particles, and, 
to a less extent, on the percentage of graphite. ... 

Silicon should be kept jvist as low as possible and still have the cast- 
ings soft enough to machine. The exact percentage will depend on 
the thickness of the casting, the character of the mould and whether 
the casting is allowed to anneal itself or is quickly shaken out after 
pouring. It may range from 0.75 per cent for very heavy work up to 
2.0 per cent for small valves, etc. It is believed that the majority of 
founders use more sihcon than is best in work of this character." 

Combined carbon has a powerful action in closing the grain and giving 
a dense iron and should be just as high as possible and still have the 
iron machinable. . . . 

Manganese had best be kept moderately high since it appears to have 
some beneficial effect in closing the grain. 

Sulphur is a powerful agent in closing the grain and is frequently 
made purposely high for this end. It is, however, a dangerous agent 
since it may cause trouble in other directions, and as a general proposi- 
tion it is better to keep the sulphur low and get necessary density by a 
proper regulation of sihcon and manganese. 

Finally, one of the best, if not the best, means of closing the grain 
of cast iron and seciuring the maximum density is by means of steel scrap 
in the mixture. This is now common practice with makers of hydrauhc 
castings, and is very effective. ... 

Shrinkage 

In considering the shrinkage of cast iron it is necessary to distinguish 
between the contraction of the fluid mass previous to and during the act 
of sohdifying and the contraction of the solid mass. The first is that 
form of shrinkage which necessitates feeding in heavy castings, and which 
so often results in shrink holes or spongy places in heavy sections of 
castings which are not fed. West calls this contraction of the fluid mass 
* shrinkage. ' 

"The contraction of the solid mass represents more nearly what is 
generally called shrinkage, this term as ordinarily used meaning the 
difference in size between the casting and its pattern. This contraction 
of the solid mass West calls ' contraction. ' 

"... It seems necessary to make some distinction between the 
total amount of fluid contraction and the tendency to form shrink holes 
in the heavy sections of small castings. At least there seems to be no 



33^ Chemical Analyses 

very definite relation between chemical composition and this latter 
property and it is often the case that an iron low in graphite and, there- 
fore, having a high fluid contraction, will give sounder castings than 
another iron high in graphite and which would, therefore, require less 
feeding in a large casting. . . . " 

"Cook has found that two irons of practically identical chemical 
composition may give very different results as regards soundness when 
poured into small castings of heavy section and the writer can confirm 
this fact from his own experience. A convenient test has been developed 
by Cook to show the tendency of any particular brand of iron to trouble 
of this sort. This test consists in making a casting in the shape of a K, 
the branches having a cross section of one inch square. On breaking 
off the oblique branches any tendency to sponginess or shrink holes will 
at once be evident in the fracture." 

"As before stated there has thus far been discovered no important 
relationship between this property and chemical composition. It rather 
appears to be something inherent in the brand of iron. . . . It is a 
curious fact that, in some instances at least, the addition of a small 
amoimt of steel scrap to the mixture will act as a partial corrective." 

"The contraction of the sohd mass does not take place uniformly as 
the casting cools but in stages which are separated by periods of less 
contraction or even of actual expansion. The total shrinkage which 
perhaps includes also a portion of the shrinkage in the fluid mass is 
conveniently obtained by Keep's test or by casting a test bar between 
iron yokes and determining the space between the end of the bar and the 
yoke after cooling." 

"This, however, tells nothing as to the manner of shrinkage or the 
temperatiu-e at which it takes place. To get this latter information we 
must determine the shrinkage curve, or in other words, the length of the 
test bar at each instant of time during cooling, starting from the instant 
when the bar has solidified just enough to have some slight strength. 
West, Keep and Turner have described forms of apparatus for making 
these curves. Fig. 91 shows some typical shrinkage curves and illus- 
trates the relationship between chemical composition and the form of 
these curves." 

"It will be noted that there are three periods of expansion separated 
by intervals during which the shrinkage takes place. The first of these 
periods of expansion is due to the separation of graphite and hence is 
greatest in the softest irons. Note that in the case A , which is a white 
iron and contains no graphite, this expansion is entirely lacking. This 
expansion takes place within the temperature range 2200° to 1800° F., 
or immediately after the iron has solidified." 



Shrinkage 



331 



"The second expansion is due to the solidification of the phosphide 
eutectic with a consequent secondary precipitation of graphite at that 
time. Evidently, this expansion is only to be expected in high phos- 
phorus irons and it will be noted that it is lacking in C, which is low in 
phosphorus, and is well marked in D, which is high in phosphorus. This 
expansion takes place within the temperature range 1800° to 1500° F." 

"The third expansion is. in the writer's opinion, due to the change of 
the iron from the 'alpha' to the 'gamma' form, since it takes place 



|20 
|>P 

X 

iU 

■-^--0 
10 

o 

I 40 

-|o50 
c 

"~ 60 
v 

CD 

J 70 

c 



\n 






xi. 




^ 


^M? 


Vp 


2%^ 


^ 


^ 




^ 


' — 


. 


■A 


r 








"\ 




N 


\ 


\ 


<r 




\ 


%sy. 


?Cf 








\ 






t^. 














\ 






''?? 


ks'' 




^-~.^ 


•..^ 








V 




















"^ 
























i 




















V 




















\ 


^ 














Ar 

A 


lalyse 


5. 

r 


n 


X 








SiUcon SO/ f.4l 3.4/ 3.98 

Su/phur tr. .01 .OS .03 

~ Phos. 0.0/ .95 .04 .25- 

Mang. tr. A3 .55 .50 

COffhr/irh ?7? 7<7 Hf, IK 




\ 


\ 












6m 


ipfi.Car 
L_ 


b. 


Z.73 


2.53 
1 


?.60 
1_„. 











50 100 150 

Time- Seconds. 

Fig. qi. 



200. 



within the temperature range 1400° to 1200° F., or about where this 
change would be expected to take place. Note that this expansion is 
greatest in high silicon irons C and D, silicon having the effect of acceler- 
ating the 'gamma' to 'alpha' change. The point at which this third 
expansion occurs probably marks the lower limit below which iron cannot 
be hardened by quenching." 

"The study of these curves is very interesting to the experimenter 
and it is believed that when we understand them better they may 
become of practical value to the foundryman. At present, however, 



33^ Chemical Analyses 

the determination of total shrinkage gives information which is of more 

immediate value." 

"The effect of composition on total shrinkage is given in concise form 

by the following tabular statement: 

Per cent 
SiHcon Decreases by about .01 inch per foot for each . 20 

Sulphur Increases by about . 01 inch per foot for each . 03 

Phosphorus . . . Decreases by about . 015 inch per foot for each . 10 

Manganese. . . . Increases by about . 01 inch per foot for each . 20 

Total carbon. .Decreases. 

"To get the minimum shrinkage an iron should be high in silicon, 
from 2 to 3 per cent depending on the thickness, high in phosphorus, say, 
0.7 s to 1.25 per cent, as low as possible in sulphur, as high as possible in 
total carbon and with only enough manganese to care for the sulphur, 
or, say, 0.3 to 0.4 per cent. This will insure high graphite and hence low 
shrinkage in the casting. The iron will, however, be rather weak and 
it is something of a problem to get in one and the same iron considerable 
strength and at the same tim^ very low shrinkage." 

"By the term 'stretch' West describes the power of cast iron to stretch 
when placed under strain during the cooling process. This property is 
undoubtedly of much importance in cast iron since there are many 
castings which are called upon to exhibit it. An extreme case which 
is commonly cited is that of pulleys, the arms of which are placed in 
tension due to the quicker coohng of the rim and which must, therefore, 
either stretch or crack. There is no. data regarding the effect of various 
metalloids of cast iron on its power of stretching but in general a soft iron 
will stretch more than a hard one. Almost the only data on this subject 
is given by West. He finds that the period of greatest stretching of 
cast iron is within the temperature range 1600° to 1200° F. 



Fusibility- 
Fusibility, or the melting point of cast iron, must not be confounded 
with its fluidity, or ease of flow when molten. Fluidity is much the more 
important of these two properties, but fusibility is of some interest, 
particularly as it gives us a means of deciding intelligently in what order 
to charge metals in the cupola. 

The investigations of Dr. Moldenke have shown that the fusibihty of 
cast iron depends primarily on its combined carbon content, and, to a 
less extent, on the amount of phosphorus present. . . . We find that 
cast iron has a melting range varying from 2000° F. for a white iron up 
to 2300° F. for gray iron containing practically no combined carbon, this 



Fusibility 



333 



difference being due probably to the presence of silicon, sulphur, phos- 
phorus and manganese. 

Since the graphite in gray iron is only in mechanical mixture with the 
iron we should, perhaps, expect it to have no effect on the melting point. 
Moreover, it combines with the iron at temperatures below the melting 
point thus increasing the combined carbon and lowering the melting 
point. For this reason gray iron melts at a lower temperature than steel 
having the same percentage of combined carbon. 



2300 



2250 



^2200 

ft) 

o 

i 

^ 2150 
2 
o. 
E 



2050 



2000 































X = 


ResoJ 


tsof 


Dr.M 


7/a'er 


Ae. 


\ 




















\ 
























./'' 


» 
















P=l.5 

X 


\ 


-^Mh' 


1.4 
















X5 






















\< 


^, 




















\ 


P=l. 

\ Mn= 


4- 
I.I 
















X 


\ 
\ 

. \ 










































> 

X 


X 

\ 




















A^ 


















X 




\ 
\ 





2 3 4 

Percent Combined Carbon. 

Fig. 92. 



As previously noted, phosphorus also has the effect of lowering the 
melting point of cast iron but it is not nearly as powerful in its action as 
combined carbon. Iron containing 6.7 per cent phosphorus would melt 
at only 1740° F., but with less phosphorus than this the melting point 
rises rapidly so that the i or 2 per cent present in commercial high phos- 
phorus irons makes very little difference in the melting point. 

Fig. 92 gives in graphic form the data of Dr. Moldenke from which 
is drawn a line representing the approximate melting point of cast iron 
of any per cent combined carbon. 



334 



Chemical Analyses 



"Table I gives the melting points with analyses of some typical 
irons and ferroalloys selected from the above data. It will be noted 
that the metalloids other than carbon and phosphorus, i.e., the silicon, 
sulphur and manganese, seem to have very little effect on the melting 
point." 

Table I. — Melting Points of Cast Irons 



Melting 

point, 

degrees F. 


Com- 
bined 
carbon, 
per cent 


Graphite, 
per cent 


vSilicon, 
per cent 


Man- 
ganese, 
per cent 


Phos- 
phorus, 
per cent 


Sulphur, 
per cent 


2030 


3.98 





.14 


.10 


.22 


.037 pig iron 


2100 


3.52 


.54 


• 47 


.20 


.20 


.036 " 


' 


2140 


2.27 


1.80 


• 45 


1. 10 


1.46 


.032 " 


* 


2170 


1.93 


1.69 


•52 


.16 


• 76 


.036 " 


' 


2200 


1.69 


2.40 


1. 81 


•49 • 


1.60 


.060 " 


• 


2210 


1.48 


2.30 


1. 41 


1.39 


• 17 


.033 " 


' 


2230 


1. 12 


2.66 


1. 13 


.24 


.089 


.027 " 


* 


2210 


.84 


3.07 


2.58 


.47 


2.12 


.051 " 


' 


2250 


.80 


3.16 


1.29 


.50 


.22 


.020 " 


' 


2280 


.13 


3.43 


2.40 


.90 


.08 


.032 " " 


2350 


1.32 




.21 


.49 


(?) 


(?) steel 


2210 


6.48 


(carbon) 


• 14 


44.59 


(?) 


(?) ferromang. 


2255 


5.02 


(carbon) 


1.65 


81.40 


(?) 


(?) ferromang. 


2190 


3.38 


• 37 


12.30 


16.98 


(?) 


(? ) silicospiegel. 


2040 


1.82 


• 47 


12.01 


1.38 


(?) 


(?) ferrosilicon 


2400 


6.80 


(carbon) 


(chromium 

62.70) 






(?) ferrochrome 


2280 






(tungsten 
39-02) 






(?) ferrotungsten 



Fluidity 

"Fluidity may be defined as ease of flow. It is synonymous with 
mobihty and opposed to viscosity. It is a property of far-reaching 
importance to the foundryman and especially to the manufactiu^er of 
small and intricate castings. Unfortunately, our means of measuring 
fluidity are not very satisfactory, and this makes it difficult to determine 
quantitatively the effect of composition upon this property. About 
the most satisfactory method is to pour fluidity strips or long strips of 
perhaps one square inch section (at one end) and tapering to nothing at 
the other. The distance which the iron runs in a mold of this form is a 
rough measure of its fluidity." 

"The factors which govern fluidity are percentage of silicon, percent- 
age of phosphorus, freedom from dissolved oxide and temperature above 
the melting point." 

"Sihcon perhaps aids fluidity by causing a separation of graphite at 
the moment of sohdification, thus, according to Field, liberating latent 



Resistance to Heat 335 

heat and prolonging the life of the metal. On this basis, high total 
carbon would also aid fluidity by increasing the amount of graphite 
separated," 

"Phosphorus is probably the most important element as regards 
fluidity, high phosphorus causing a marked increase in this property. 
The best results are obtained with about 1.5 per cent phosphorus, 
although for other reasons it is seldom desirable to use as much as that." 

"Freedom from oxide is a very important point as its presence makes 
the metal sluggish and causes it to set quickly. It is a frequent and often 
unsuspected source of trouble. Dissolved oxide may be eliminated by 
any of the methods described." 

"The temperature above the freezing point is probably the most 
important factor of all in connection with fluidity, and it should here be 
noted that a distinction is made between freezing point and melting 
point. The two may coincide in the case of white iron, but will not 
usually, especially with gray iron. This is because, as we have already 
seen, gray irons have a melting temperature corresponding to their per- 
centage of combined carbon rather than total carbon. After they are 
in the molten state, however, all the carbon is in solution (combined as 
far as melting points are concerned), hence, the freezing point will corre- 
spond more nearly to the melting point of a white iron having the per- 
centage of combined carbon equal to the total carbon of the original gray 
iron. This will be in general from 100° to 300° lower than its melting 
point. For this reason when gray irons are melted they are always 
considerably superheated above their solidifying points, and the greater 
this superheat, the more fluid the iron. Evidently, the superheat due 
to this cause will be the greater the lower the combined carbon in the 
iron going into the cupola." 

Practical rules for getting fluid iron are as follows: 

"Keep the phosphorus high, — up to i.oo to 1.25 if possible." 

"If the work will permit, use a soft iron of 2 per cent or over in silicon, 
and low in combined carbon." 

"Avoid oxidizing conditions in melting and, if necessary, use deoxidiz- 
ing agents." 

"Use plenty of coke and good cupola practice." 

Resistance to Heat 

"Ability to withstand high temperatures is of paramount importance 
in several classes of castings such as grate bars, ingot moulds, anneahng 
boxes, etc., and the factors which affect this ability are, the percentage 
of phosphorus, sulphur and combined carbon, and the density or close- 
ness of grain." 



336 Chemical Analyses 

"Phosphorus forms with iron an alloy which melts at only 1740° F., or 
about 400° lower than cast iron free from phosphorus, and each per cent 
of phosphorus present gives rise to 15 per cent of this easily fusible con- 
stituent. Now, it will be evident that the presence of a molten con- 
stituent in a piece of iron must greatly weaken it, and hence it is that the 
presence of much phosphorus decreases the resistance of cast iron to 
heat." 

"Sulphur acts in a similar manner to phosphorus since it also forms 
with iron a constituent of low melting point (1780° F.). It is, therefore, 
detrimental to castings which have to stand high temperatures." 

"As previously. noted, combined carbon is the element which more than 
any other determines the melting point of cast iron, this melting point 
becoming lower with increase in this element. It would seem then, that 
combined carbon must be very detrimental in this class of castings. 
However, it should be remembered that the condition of the carbon in 
the solid iron changes readily at high temperatiures, and, hence, after the 
casting has been in use for a while its combined carbon content will not 
in general be the same as when cast. This fact makes the question of 
combined carb6n of much less practical importance than either phos- 
phorus or sulphur." 

"Density or close grain is commonly stated to render cast iron con- 
siderably more resistant to the effects of heat. . . . " 

"One feature of the effect of heat on cast iron which deserves especial 
mention is the permanent expansion which it imdergoes on repeated 
heatings. This peculiar behavior was first discovered by Outerbridge 
and has since been also investigated by Rugan and Carpenter." 

"The extent to which this growth may take place is certainly sur- 
prising, the increase being in some cases as high as 46 per cent by volume 
and 1% inches in the length of a 15-inch bar. The strength of the metal 
is decreased proportionately to the expansion or to about one-half of the 
original strength. Both the expansion and the decrease in strength are 
explained by microscopic examination, which shows minute cracks 
throughout the interior of the metal. . . ." 

"Two conditions are necessary for this growth. First, repeated 
heatings, and second, a proper composition of the metal." 

"With regard to the heating, a minimum temperature of 1200° F. is 
necessary. At 1400° to 1600° the rate of growth is more rapid and an 
increase in temperature beyond 1700° produces no additional effect. 
Both heating and cooHng are necessary to procure the growth, and the 
time of heating makes very little difference. No greater growth was 
produced by 17 hours continuous heating than by 4 hours. The num- 
ber of heatings required to produce the maximum amount of growth 



Resistance to Heat 337 

varies with different irons, but usually lies somewhere between 50 and 
100." 

"Regarding the effects of composition, it appears that the growth is 
favored by the presence of graphite and silicon, and also by a large grain 
or open structure. White iron containing no graphite expands slightly 
when subjected to this treatment but not sufi&ciently to overcome its 
original shrinkage. In this case the expansion is due to the conversion 
of the combined carbon into the temper form, or in other words, to the 
malleableizing of the casting. Soft irons low in combined carbon and 
high in silicon show the greatest increase in volume. The effects of 
sulphur, manganese and phosphorus have not been investigated. Steel 
and wrought iron are not subject to this growth, but on the contrary 
undergo a slight permanent contraction when repeatedly heated." 

"It is evident that this property of cast iron is of great importance in 
many of the applications of the metal and limits its use for many pur- 
poses. It is, no doubt, the reason why a close-grained iron gives better 
results when exposed to high temperatures and affords an explanation 
for the warping of grate bars, annealing boxes and similar castings. It 
also shows why chills and permanent molds must not be allowed to be 
heated to redness, such a degree of heat resulting in permanent expansion 
and the loss of their original dimensions." 

The following is a summary of some of the published statements 
regarding the proper composition for castings exposed to high tempera- 
tures: 

"Cast iron to withstand high temperatures should be low in phos- 
phorus and combined carbon." 

"In car wheels manganese increases the resistance to heat strain." 

"For refractory castings choose a fine grained cast iron, best contain- 
ing about 2 per cent manganese to retard the separation of amorphous 
carbon." 

"Castings to resist heat should contain about 1.80 per cent silicon, 
0.03 per cent sulphur, 0.70 per cent phosphorus, 0.60 per cent%ianganese 
and 2.90 per cent total carbon. Low sulphur is of chief importance, low 
silicon, carbon and manganese are also advisable." 

"Close-grained cast iron having the greatest density will invariably 
be found best to withstand chemical influences and high temperatures," 

"A chill which had given excellent service had the following composi- 
tion: silicon, 2.07 per cent; sulphur, 0.073 per cent; phosphorus, 0.03 
per cent; manganese, 0.48 per cent; combined carbon, 0.23 per cent; 
graphite carbon, 2.41 per cent; total carbon, 2.64 per cent. • 

" Two permanent moulds which had given excellent service analyzed 
as follows : 



338 



Chemical Analyses 



Silicon, 
per cent 


Sulphvir, 
per cent 


Phosphorus, 
per cent 


Manganese, 
per cent 


Combined 
carbon, 
per cent 


Graphite, 
per cent 


Total 
carbon, 
per cent 


2. IS 
2. 02 


.086 
.070 


1.26 
.89 


-41 
.29 


.13 

.84 


3.17 
2.76 


3.30 
3.60 



"Ingot moulds and stools are best made from medium soft iron low in 
phosphorus, or what is termed a regular Bessemer iron. ... ." 

Electrical Properties 

"Of the three electrical properties, conductivity, permeability and 
hysteresis, the second only is of importance in connection with cast iron. 



B 






















12.000 










































10,000 






































^^' 


^ 


e;0oo 










^. 


1?..' 


;;: 




^. 


^- 










:^ 


c 


^'^ 








'6,000 






9 




,y^ 














^y 


/ 


> 














4,000 


/ 
/ 
/ i 


7 . 

/ 


/ 
















// 
// 


/ 


















2,000 


!/ 




















' 






















V 





















20 



40 60 

Fig. 93. 



80 



Little is known regarding the relation between chemical composition 
and conductivity of cast iron. In the case of steel it has been found that 
manganese is the element most injurious to this property with carbon 
a close second. Hence, by analogy, we may infer that to make iron 
castings of high conductivity we should keep both the manganese and 
combined carbon as low as possible. 



Electrical Properties 



339 



Permeability may be defined as magnetic conductivity and is of 
importance in many castings used in the construction of electrical 
machinery. Permeability data are generally given in the form of a 
curve expressing the relation between the magnetizing force H and the 
resulting field strength or number of lines of magnetic force per unit 
area B. This is known as the permeabihty curve. The permeabihty 

is the ratio ^ and it will be noted that it is different for each value of the 
B 

magnetizing force, H, but approaches a constant or saturation value for 

high values of U. See Fig. 93. 





























160 








.,S 




924 






n'2 












1 


fs 




T 


I^^ 


P" 


y 








13, 
140 


H 


--^ 


f\ 


^ 


^J^' 


^r 


/ 


jT 










10^ 


n^ 


19 


►)7 


^ 


^ 
















rfcd 


120 




4 


\ 










N 


3. Sii. Pho5. Mang. 

1.79 .75 .19 






^ 


^ 








. 


i 1.76 .75 1.73 
1- 1.81 .75 1.05 
J 178 75 I 01 


100 










i.^^ 








a 1.76 .75 3.46 
7 1.75 .75 .35 
i 2.70 ■ .75 .-^fi 










\ 






9 2.61 .75 .35 

10 lis .75 ,36 

11 3.67 .76 .36 


80 












\ 






3 1.49.09.75- .46. 

4 1.49 .16 .75 .49 














\ 




6 Z,09 .85.75 .4B 

7 2.08 1.35.75 .43 

8 2.14 3.18.75 .43 


60 














6^ 


^ 9 ).6Z .91 .47 

to 1.69 l.ll .49 
21 1.63 I.7S .43 


















23 1.84 Z.SS .SZ 

24 1.76 ?.6I • .54 
























1 



1.0 



2.0 3.0 

Fig. 94. 



4.0 



6.0 



The effects of the various elements on permeability are not yet entirely 
clear although there are some published data along this line. The writer 
has recentfy done considerable work on the relation between permeability 
and chemical composition of cast iron, and the resiilts, as yet unpubHshed, 
are summarized in Fig. 94. It will be noted that the effects of silicon, 
phosphorus and aluminum are not well marked and are probably not of 



340 Chemical Analyses 

any very great importance. On the other hand, manganese has a very 
detrimental effect on this property. 

Silicon has the opposite effect from manganese in that it accelerates 
this change in the form of the iron, and we would, therefore, expect 
it to have a more or less beneficial influence. Silicon steel has 
achieved a wide reputation as a high permeability material for use in 
the construction of tran former cores, etc. According to the author's 
results high silicon is particularly effective in increasing B for low values 
oiH. 

An important element not considered in the diagram, Fig. 94, is 
carbon. For high permeability the lower the carbon the better, and 
excellent results are now being obtained through the use of semi-steel for 
electrical castings. In this connection, however, it must be remembered 
that manganese is undesirable and hence must be used cautiously as a 
deoxidizer in this class of work. 

Some practical rules for obtaining high permeability iron are given 
herewith. 

Keep the silicon high, best in the neighborhood of 3 per cent. 

Keep the manganese low, preferabl}^ below 0.5 per cent. 

If practicable keep the carbon low by the use of steel scrap or air 
fiirnace iron. 

Allow the castings to anneal themselves, i.e., cool completely in the 
sand before shaking out. 

Hysteresis, like conductivity, is seldom or never of importance in cast 
iron. The property may be defined as the loss of energy due to molecular 
friction when magnetic polarity is reversed. The effect of composition 
upon hysteresis is in general about the same as in the case of permeability. 

Resistance to Corrosion 

Although there are a great many corrosive agencies it is not practicable, 
because of lack of information, to treat of each separately, and so far as 
we know the effects of composition woiild be relatively the same for the 
various corroding agents. 

The following is a summary of most of the published information 
along this line: 

Pig iron which best resists acids contains silicon, i.o per cent; phos- 
phorus, 0.5 per cent; sulphur, 0.05 per cent; carbon, 3.0 per cent. 

Excellent results with respect to resistance to corrosion by acids were 
obtained through the use of a mixture of three brands of pig iron.^, B 
and C in the proportion, two parts of A, one part B and one part C 
The analysis of the pig irons is thus given: 



Resistance to Corrosion 



341 



Fracture 


Silicon, 
per cent 


Manganese, 
per cent 


Phosphorus, 
per cent 


Total 
carbon, 
per cent 


A Dark gray 


3. SO 
I -SO 

.70 


■ 50 
.40 

•25 


.20 
.20 
.20 


3.80 
3.50 
3.50 


B Light Gray . 


C Mottled. 





The composition of acid-resistant castings should be about as follows: 



Silicon, 
per cent 


Sulphur, 
per cent 


Phosphorus, 
per cent 


Manganese, 
per cent 


Total carbon, 
per cent 


.8 to 2.0 


.02 to .03 


.40 to .60 


I to 2.0 


3.0 to 3.5 



and in addition, the metal should be as free as possible from oxide. 

Cast iron to withstand the corrosive action of molten chemicals 
should be close grained and dense. The iron having the greatest den- 
sity will invariably be found to best withstand chemical influences and 
high temperatures. The addition of deoxidizing agents is of great 
benefit. 

Gray iron is attacked by acids about three times as fast as white iron. 
In cases where it is not practicable to use white iron castings it is some- 
times possible to cast against chills in such a manner as to form a white 
iron surface to resist corrosion and still leave the body of the casting 
gray. 

In a series of tests on the acid-resisting properties of some well-known 
EngHsh brands of iron, the No. i iron, presumably high in silicon, and 
the "hematite," low in phosphorus and probably high in siUcon, gave the 
best results. 

Ferrosilicons with high percentages of silicon, 20 per cent and over, are 
remarkably resistant to the effects of acids and are being made into 
vessels for use in the chemical industries. 

Sulphur has been found to be a source of corrosion in steel in some 
instances, causing pitting at points where manganese sulphide has 
segregated. 

It has been shown that the presence of small amounts of copper in 
steel and puddled iron diminish their tendency to rust. 

Some practical rules for obtaining castings resistant to corrosion are 
as follows : 

Use white iron if practicable. 



342 Chemical Analyses 

If not practicable to use white iron casting, chill those surfaces which 
are to be in contact with the corrosive substances. 

If gray iron must be used get dense, close-grained castings through 
the use of steel scrap or otherwise. 

Avoid oxidized metal, use good cupola practice and good pig irons. 

If possible use deoxidizing agents. 

Keep the sulphur just as low as possible. 

Resistance to Wear 

We must first make some distinction between two cases of wear 
typified by a grinding roll and a brake shoe. The first case may be 
dismissed by the simple statement that the greater the hardness the 
better the wear, providing at the same time that the iron is sufficiently 
strong. 

In the second case, however, it is necessary that the casting should not 
be so hard as to unduly wear the material with which it comes in contact. 
For example, the brake shoe must be softer than the tread of the car 
wheel. There is no theory to guide us in the matter and the rules given 
are the results of experiment chiefly with brake shoes. 

Too much silicon gives an open, soft iron which does not wear well. 
The best results are obtained with silicon about iH per cent in castings 
of medium thickness. 

Sulphur is claimed by many to be advantageous in castings for fric- 
tional wear because it closes the grain and hardens somewhat. Diller 
records a peculiar occurrence of a hard spot which could not be machined, 
a smooth surface being formed which wore the drill although it could be 
dented with a center punch. Analysis showed 0.20 per cent sulphur and 
0.50 per cent combined carbon. 

Phosphorus is best kept moderately low. Most specifications call for 
0.75 per cent or under. It is injurious probably because it weakens the 
iron at the high temperature sometimes produced by friction. 

Manganese is best kept moderately high to take care of the sulphur. 
Most brake shoe specifications call for under 0.70 per cent. 

The addition of steel scrap to the mixture has been found to give 
excellent results for this class of work, probably owing to the reduction 
in the total carbon and to its action in closing the grain. 

Coefficient of Friction 

There are no data as to the relation between the composition of cast 
iron and its coefficient of friction. Since graphite is an excellent lubri- 
cant it is probable that the percentage of graphite is the controlling 
factor here, the friction decreasing with increase in this element. From 



Casting Properties 343 

theoretical considerations we should expect the best results to be obtained 
with a very soft iron low in sulphur, manganese and combined carbon 
and high in graphite. 

Casting Properties 

The properties which remain to be considered pertain more par- 
ticularly to the casting as a whole and are chiefly influenced by the design, 
moulding and pouring of the casting, and to a very much less extent, by 
the composition of the metal. 

Unsoundness due to the presence of blow-holes and shrinkage cavities, 
while usually resulting from bad practice in moulding may also be caused 
by poor quality of metal. Blowholes may be caused by oxidized metal 
or by excessive sulphur. . . . When caused by sulphur the remedy is 
to decrease this element. Raising the manganese is often effective in 
preventing blowholes since it acts both as a deoxidizer and desulphurizer. 
Scott states that manganese below 0.25 per cent often results in blow- 
holes. High phosphorus sometimes acts as a corrective of blowholes due 
to its prolonging the fluidity, thus giving the iron more chance to release 
the dissolved gases. 

Dirty castings are also caused chiefly by poor moulding, pouring or 
cupola practice. Occasionally, however, it may result from wrong 
composition of the metal, and the points chiefly to be watched are to keep 
the sulphur low; to avoid kish or segregated graphite and to avoid 
oxidized metal. 

Sulphur tends to cause dirty castings because it makes the iron congeal 
more quickly, and hence any dirt present has less chancy to separate. 
In addition, the sulphides of iron and manganese themselves form dirt 
spots when segregated. Kish is usually caused by too much silicon, or 
sometimes by too much total carbon. Oxidized metal is a prolific source 
of dirty castings, but the oxidization is usually due to bad cupola practice, 
or to the use of oxidized scrap. Moderately high manganese and phos- 
phorus are conducive to clean castings, the first because it takes care of 
sulphur and oxidation, and the second because it increases the fluidity of 
the metal and thus gives the dirt a better chance to float out. 

Porosity is usually caused by the presence of kish (see preceding 
paragraph). Pinholes, another form of porosity, are usually due to 
excessive sulphiir in the form of iron sulphide. This compound retains 
gases in solution until the metal is partially frozen and then releases 
them in the form of tiny bubbles which give rise to this defect. Decrease 
in sulphur or increase in manganese or both is the remedy. 

Segregation proper is caused by the difference in melting point and 
specific gravity of the several constituents of cast iron. The constit- 



344 Chemical Analyses 

uents of lowest melting point are the phosphorus and sulphur compounds, 
and it is, therefore, in these cases that we find the greatest tendency 
towards segregation. It is not unusual to find hard spots in heavy 
castings high in phosphorus which are caused by the phosphide being 
squeezed out into blow-holes formed during solidification. Frequently 
the phosphide does not completely fill the cavity, or fills it as a loose 
globule. The sulphides, owing to their low specific gravity, usually 
segregate in the top of the casting and it is not infrequent to find sev- 
eral times the normal amount of sulphur in the upper part of heavy 
castings. Manganese sulphide segregates more readily than iron sul- 
phide. 

Besides segregation proper we sometimes find cases of non-homo- 
geneity due to other causes. Occasionally spots of white iron are found 
in the interior of castings. It has always been difficult to account for 
these but the clew is given by the fact that they are invariably found in 
castings poured from the first metal tapped. 

Undoiibtedly they are caused by the iron boiling on the sand bed and 
are connected in some way with the partial Bessemerizing of the metal. 
Again, hard spots in castings are sometimes due to small pieces of metal 
(for example, small steel scrap and shot iron) being incompletely melted 
in their passage through the cupola. Ferromanganese and other ferro- 
alloys may give rise to this same trouble through incomplete solution 
when stirred into the ladle. 

Shrinkage strains are caused primarily by wrongly designed castings, 
but the trouble may be aggravated by the composition of the metal. 
High sulphur is a particularly prolific source of internal stresses, and, 
in general, the greater the total shrinkage, the greater the strains due to 
this cause. 

As all foundrymen know, the fineness of finish and smoothness of skin 
of a casting depend chiefly on the sands and facings used and the skill 
of the moulder. High phosphorus in the iron, however, is a consider- 
able aid in getting the fine skin desired in ornamental work. Another 
element affecting the skin is manganese which has the rather peculiar 
action of causing the sand to peel from the castings with extreme readi- 
ness. With I per cent manganese this tendency is evident and with 
2 per cent it is very marked. 

Bars, plates and hollow castings were treated, which were permitted 
to cool in the moulds. The plates cooled more slowly than the bar 
samples and the material proved somewhat softer, giving smaller values 
for the bending, tensile and compressive strength, but was better as 
regards flexure and strength to resist impact. 

Tests reported to the Iron and Steel Institute showed : 



Notes on the Micro-structure of Cast Iron 345 

The best tensile and* transverse tests are obtained from bars which 
have been machined. 

Transverse test bars cast on edge and tested with the "fin" in com- 
pression give the best results. 

The transverse test is not so reliable or helpful as that of the moment 
of resistance. 

Cast iron gives the best results when poured as hot as possible. 

As in some measure explanatory of the conflicting results obtained in 
testing bars of precisely the same chemical combination, and as showing 
the importance of microscopical examinations of the structure of cast 
iron in pointing out the causes of difference in its physical properties, the 
paper of Mr. Percy Longmuir published in the Journal of the American 
Foundrjrmen's Association, June, 1903 is given in full. 

Notes on the Micro-structure of Cast Iron 

By Percy Longmuir, Sheffield, England 

Journal of the American Foundrymen's Association, Vol. XII, June, IQ03. 

Instances are occasionally found where metal of the right chemical 
composition goes wrong in practice. It is in cases of this kind that the 
real value of microscopical examination is most evident, for very often 
such an examination will locate the trouble and at the same time suggest 
a remedy. Naturally an examination of diseased samples can only be 
undertaken after a thorough study of healthy ones, hence a foundation 
for the study of abnormal samples must necessarily be based on the 
knowledge gained from a wide series of normal ones, that is, samples of 
known chemical composition and known physical conditions. 

The structoare of cast iron is very complex — far more so than that of 
steel — a fact readily shown by the high content of elements present 
other than iron. By polishing and etching a sample of cast iron, several 
of the compounds of the elements with iron are, under suitable magni- 
fication, rendered visible. The structural features, such as the arrange- 
ment and distribution of the various compounds and their relationship 
to each other, can then be readily noted and the effect of this combination 
on the mass then becomes an estimable quantity. 

If the metal under examination contain no impurities it is evident that 
its mass will be built up of pure crystals. A section cut from such a pure 
metal will, after polishing and etching, show only the crystal junctions. 
Crystal junctions of this type are shown in Fig. 95 , which represents the 
structure of almost pure iron. Even here, although the metal is so pure, 
the very minute trace of carbon present can be readily detected in the 
dark knots of which about a dozen are to be seen. As foreign elements 



346 



Chemical Analyses 



are added to pure iron the structure becomes more complex and a point 
is reached when all the pure crystals are replaced by more complex ones. 
It is to be remembered that all gray irons contain appreciable amounts 
of two varieties of carbon, silicon, manganese, sulphur and phosphorus. 

=13 




— Magnified 360 diameters 






0.03 
0.02 
0.07 


Sulphur 

Phosphorus 

Iron 






99 


01 

01 
86 



Fig. 95. 
Carbon 
Silicon 
Manganese 

Of these elements graphite is present in its elementary form, that is, as 
free carbon. The remaining constituents are present in compound form 
associated either with iron or with other elements. Thus sulphur may 
occur as sulphide of manganese or as iron sulphide. Carbon occurring 




Fig. 96. — Magnified 60 diameters. 
Combined Carbon o . 54 Manganese 

Graphite 3 . 1 1 Sulphur 

Silicon 1.77 Phosphorus 



0.63 
0.04 
1-34 



in the combined form is present as a definite carbide of iron; or under 
certain conditions as a double carbide of iron and manganese. Phos- 
phorus is associated with iron as a definite phosphide. These compounds 
are all distinguishable under suitable magnification, but the association 
of silicon and iron is, so far as present knowledge goes, unrecognizable. 



Notes on the Micro-structure of Cast Iron 



347 



Microscopically these constituents have received other names — for 
instance pare iron is known as "ferrite," hence a structure similar to 
that of Fig. 96 consists almost entirely of ferrite. Combined carbon 
receives the term "cementite" and a mixture of cementite and ferrite 





Fig. 97. — Magnified 460 diameters. Fig. 98. — Magnified 360 diameters. 

is known as "pearlite." Pearlite often consists of alternate striae of 
cementite and ferrite and in such a form gives a magnificent play of 
colors resembling those of mother-of-pearl, consequently this constituent 
was named by its discoverer, Dr. Sorby, the "pearly constituent," a term 
now contracted to "pearhte." ' 




Fig. 99. — Magnified 50 diameters. 

Combined Carbon 3 . 25 Sulphur 0.41 

Silicon 0.78 Phosphorus 0.06 

Manganese o . 09 

The classical researches of Professor Arnold have conclusively shown 
that iron containing 0.89 per cent carbon consists entirely of pearlite. 
As the content of carbon increases above 0.89 per cent, structurally free 
cementite appears increasing in quantity with each increment of carbon. 
It therefore follows that a white cast iron will consist essentially of 



34^ Chemical Analyses 

cementite and pearlite. In the majority of gray irons used in the found- 
ries the conibined carbon is well below 0.89 per cent — cementite is, 
therefore, only present as a constituent of pearlite. 

Sulphide globules when in the form of manganese sulphide show a light 
gray color, while iron sulphide shows a hght brown tint. 

In high sulphur irons the sulphide tends to envelop the crystals; a 
section cut from such an iron would show a network of sulphide following 
the crystal junctions and destroying their continuity. These siilphides 
have been thoroughly investigated by Professor Arnold whose researches 
have thrown much light on the behaviour of both iron and manganese 
sulphide. 

The relations of iron and phosphorus have been very thoroughly 
studied by Mr. J. E. Stead. In September, 1900, Mr. Stead presented 




Fig. 100. — Magnified 50 diameters. 

Combined Carbon 0.82 Manganese 0.09 

Graphite 2.07 Sulphur 0.37 

Sihcon 0.75 Phosphorus 0.07 

before the Iron and Steel Institute a most exhaustive research on this 
subject. With ordinary pig irons the phosphide of iron appears to be 
rejected to a eutectic of uncertain composition. Eutectic may for our 
purpose be defined as that portion last to sohdify. This phosphide 
eutectic may be readily distinguished in all gray irons by an ordinary 
etching medium, but in white irons containing structurally free cementite, 
Mr. Stead's "heat tinting" process becomes necessary to distinguish the 
eutectic from the cementite. 

Fig. 96 reproduces a photo-microscope of an unetched section of gray 
iron at a magnification of 60 diameters. 

This magnification gives, as it were, a general view only — to get at the 
ultimate structure higher powers must be used. Fig. 97 represents the 
structure of an ordinary gray iron magnified 460 diameters. The larger 



Notes on the Micro-structure of Cast Iron 



349 



portion of this field consists of pearlite embedded in which are irregular 
areas of the phosphide eutectic and several notable black plates of 
graphite. The phosphide eutectic is recognizable by its irregular shape 
and broken up structure; an area in the center of the photograph enclos- 
ing an area of pearlite is worthy of notice. 

Fig. 98 reproduces an area of phosphide eutectic from the same section 
as Fig. 96. 

A typical white cast iron consisting essentially of pearlite and cementite 
is shown in Fig. 99. This is a type of iron used as a base for the production 
of malleable cast iron. 

The influences of annealing are shown in Fig. 100, which represents the 
same iron as Fig. 99, after going through the ordinary malleable iron 




Fig. ioi. — Magnified 60 diameters. 



annealing in ore. This section consists essentially of pearlite and 
graphite — the analyses appended to each figure showing the change in 
carbon condition. For the loan of the negatives illustrating Figs. 99 
and 100, the writer is indebted to the courtesy of Mr. T. Baker, B. Sc. 
Quite apart from the clear light thrown on what has been aptly termed 
the internal architecture of a metal, microscopical examination reveals 
many other features of profitable interest, one notable feature being the 
examination of minute flaws. Space will not permit of many illustra- 
tions under this head, but Fig. loi, reproduced from a photo-nlicrograph 
of a pin-hole in the same section as Fig. 96, will show the range of possi- 
bility in this direction. Obviously, a study of flaws of this character 
offers much to the founder producing castings which have to meet a 
hydraulic or high steam pressure test. 



CHAPTER XIV 



Standard Specifications for Cast Iron Car Wheels 

Chemical Properties 
The wheels furnished under this specification must be made from the 
best materials and in accordance with the best foundry methods. The 
following pattern analysis is given for information, as representing 
the chemical properties of a good cast iron wheel. Successful wheels, 
varying in some of the constituents quite considerably from the figures 
given, may be made: 



Analysis 


Per cent 


Analysis 


Per cent 


Total carbon 


3.50 

2.90 

.60 

.70 


Manganese 

Phosphorus 

Sulphur 


40 


Graphitic carbon 


.50 
08 


Silicon .... 











1. Wheels will be inspected and tested at the place of manufacture. 

2. All wheels must conform in general design and in measurements 
to drawings which will be furnished, and any departure from the stand- 
ard drawing must be by special permission in writing. Manufacturers 
wishing to deviate from the standard dimensions must submit duplicate 
drawings showing the proposed changes, which must be approved. 

Drop Tests 

3. The following table gives data as to weight and tests of various 
kinds of wheels for different kinds of cars and service: 



Wheel 


33-inch diameter freight and pas- 
senger cars 


36-inch diameter 






Kind of service ...\ 


60,000 lbs. 

capacity 

and less 

I 

600 


70,000 lbs. 
capacity 

2 
650 


100,000 lbs. 
capacity 

3 

700 


Passenger 
cars 

4 
700 lbs. 


Locomotive 
tenders 

5 
750 lbs. 


Desired . . . 
Weight \ 

Variation . 


Two per cent either way 


Height of drop, feet. 
Number of blows . . . 


9 
10 


12 
10 


12 
12 


12 
12 


12 
14 



350 



Material and Chill ^ 351 

Marking 

4. Each wheel must have plainly cast on the outside plate the name 
of the maker and place of manufacture. Each wheel must also have 
cast on the inside double plate the date of casting and a serial foundry 
number. The manufacturer must also provide for the guarantee mark, 
if so required by the contract. No wheel bearing a dupUcate number, or 
a number which has once been passed upon, will be considered. Num- 
bers of wheels once rejected will remain unfilled. No wheel bearing an 
indistinct number or date, or any evidence of an altered or defaced 
number will be considered. 

Measures 

5. All wheels offered for inspection must have been measured with a 
standard tape measure and must have the shrinkage number stenciled 
in plain figures on the inside of the wheel. The standard tape measure 
must correspond in form and construction to the "Wheel Circumference 
Measure" established by the Master Car Builders' Association in 1900. 
The nomenclature of that measure need not, however, be followed, it 
being suflQcient if the graduating marks indicating tape sizes are one- 
eighth of an inch apart. Any convenient method of showing the shrink- 
age or stencil number may be employed. Experience shows that 
standard tape measures elongate a little with use, and it is essential to 
have them frequently compared and rectified. When ready for inspec- 
tion, the wheels must be arranged in rows according to shrinkage numbers, 
all wheels of the same date being grouped together. Wheels bearing 
dates more than thirty days prior to the date of inspection will not be 
accepted for test, except by permission. For any single inspection and 
test, only wheels having three consecutive shrinkage or stencil numbers 
will be considered. The manufacturer will, of course, decide what three 
shrinkage or stencil numbers he will submit in any given lot of 103 wheels 
offered, and the same three shrinkage or stencil numbers need not be 
offered each time. 

Finish 

6. The body of the wheels must be smooth and free from slag and 
blowholes, and the hubs must be solid. Wheels will not be rejected 
because of drawing around the center core. The tread and throat of the 
wheels must be smooth, free from deep and irregular wrinkles, slag, sand 
wash, chill cracks or swollen rims, and be free from any evidence of hollow 
rims, and the throat and tread must be practically free from sweat. 

Material and Chill 

7. Wheels tested must show soft, clean, gray iron, free from defects, 
such as holes containing slag or dirt more than one-quarter of an inch in 



352 Standard Specifications for Cast Iron Car Wheels 

diameter, or clusters of such holes, honeycombing of iron in the hub, 
white iron in the plates or hub, or clear white iron around the anchors of 
chaplets at a greater distance than one-haK of an inch in any direction. 
The depth of the clear white iron must not exceed seven-eighths of an 
inch at the throat and one inch at the middle of the tread, nor must it be 
less than three-eighths of an inch at the throat or any part of the tread. 
The blending of the white hon with the gray iron behind must be without 
any distinct line of demarcation, and the iron must not have a mottled 
appearance in any part of the wheel at a greater distance than one and 
five-eighths inches from the tread or throat. The depth of chill will be 
determined by inspection of the three test wheels described below, all 
test wheels being broken for this purpose, if necessary. If one only of 
the three test wheels fails in limits of chill, all the lot under test of the 
same shrinkage or stencil number will be rejected and the test will be 
regarded as finished so far as this lot of 103 wheels is concerned. The 
manufacturer may, however, offer the wheels of the other two shrinkage 
or stencil numbers, provided they are acceptable in other respects as 
constituents of another 103 wheels for a subsequent test. If two of the 
three test wheels fail in limits of chill, the wheels in the lot of 103 of the 
same shrinkage or stencil number as these two wheels will be rejected, 
and, as before, the test will be regarded as finished as far as this lot of 
103 wheels is concerned. The manufacturer may, however, offer the 
wheels of the third shrinkage or stencil number, provided they are 
acceptable in other respects, as constituents of another 103 wheels for 
a subsequent test. If all three test wheels fail in limits of chill, of course 
the whole hundred will be rejected. 

Inspection and Shipping 

8. The manufacturer must notify when he is ready to ship not less 
than 100 wheels; must await the arrival of the inspector; must have a 
car, or cars, ready to be loaded with wheels, and must furnish facilities 
and labor to enable the Inspector to inspect, test, load and ship the 
wheels promptly. Wheels offered for inspection must not be covered 
with any substance which will hide defects. 

9. One himdred or more wheels being ready for test, the inspector will 
make a list of the wheel numbers, at the same time examining each wheel 
for defects. Any wheels which fail to conform to specifications by 
reason of defects must be laid aside, and such wheels will not be accepted 
for shipment. As individual wheels are rejected, others of the proper 
shrinkage or stencil number may be offered to keep the number 
good. 



Thermal Test 353 

Retaping 

10. The inspector will retape not less than 10 per cent of the wheels 
offered for test, and if he finds any showing wrong tape-marking, he will 
tape the whole lot and require them to be restenciled, at the same time 
ha\dng the old stencil marks obliterated. He will weigh and make check 
measurements of at least 10 per cent of the wheels offered for test, and 
if any of these wheels fail to conform to the specification, he will weigh 
and measure the whole lot, refusing to accept for shipment any wheels 
which fail in these respects. 

Drop Tests 

11. Experience indicates that wheels with higher shrinkage or lower 
stencil numbers are more apt to fail on thermal test; more apt to fail 
on drop test and more apt to exceed the maximum allowable chill than 
those with higher stencil or lower shrinkage numbers; while, on the 
other hand, wheels with higher stencil or lower shrinkage mmibers are 
more apt to be deficient in chill. For each 103 wheels apparently 
acceptable, the inspector will select three wheels for test — one from 
each of the three shrinkage or stencil numbers offered. One of these 
wheels chosen for this purpose by the inspector must be tested by drop 
test as follows: The wheel must be placed flange downward in an anvil 
block weighing not less than 1700 pounds, set on rubble masonry two 
feet deep and having three supports not more than five inches wide for 
the flange of the wheel to rest on. It must be struck centrally upon the 
hub by a weight of 200 pounds, falhng from a height as shown in the 
table on page 350. The end of the falling weight must be flat, so as to 
strike fairly on the hub, and when by wear the bottom of the weight 
assumes a roimd or conical form, it must be replaced. The machine for 
making this test is shown on drawings which will be furnished. Should 
the wheel stand, without breaking in two or more pieces, the niraiber of 
blows shown in the above table, the one hundred wheels represented by 
it wiU be considered satisfactory as to this test. . Should it fail, the whole 
hundred will be rejected. 

Thermal Test 

12. The other two test wheels must be tested as follows: The wheels 
must be laid flange down in the sand, and a channel way one and one-half 
inches in width at the center of the tread and four inches deep must be 
molded with green sand around the wheel. The clean tread of the wheel 
must form one side of this channel way, and the clean flange must form 
as much of the bottom as its width will cover. The channel way must 



354 Standard Specifications for Cast Iron Car Wheels 

then be filled to the top from one ladle with molten cast iron, which must 
be poured directly into the channel way without previous cooling or 
stirring, and this iron must be so hot, when poured, that the ring which 
is formed when the metal is cold shall be sohd or free from wrinkles or 
layers. Iron at this temperature will usually cut a hole at the point of 
impact with the flange. In order to avoid spitting during the pouring, 
the tread and inside of the flange during the thermal test should be 
covered with a coat of shellac; wheels which are wet or which have been 
exposed to snow or frost may be warmed sufficiently to dry them or 
remove the frost before testing, but under no circumstances must the 
thermal test be applied to a wheel that in any part feels warm to the 
hand. The time when pouring ceases must be noted, and two minutes 
later an examination of the wheel under test must be made. If the wheel 
is found broken in pieces, or if any crack in the plates extends through 
or into the tread, the test wheel will be regarded as having failed. If 
both wheels stand, the whole hundred will be accepted as to this test. 
If both fail, the whole hundred will be rejected. If one only of the ther- 
mal test wheels fails, all of the lot under test of the same shrinkage or 
stencil number will be rejected, and the test will be regarded as finished, 
so far as this lot of wheels is concerned. The manufacturer may, however, 
offer the wheels of the other two shrinkage or stencil numbers, provided 
they are acceptable in other respects, as constituents of another 103 
wheels for a subsequent test. 

Storing and Shipping 

13. All wheels which pass inspection and test will be regarded as 
accepted, and may be either shipped or stored for future shipment, as 
arranged. It is desired that shipments should be, as far as possible, in 
lots of 100 wheels. In all cases the inspector must witness the shipment, 
and he must give, in his report, the numbers of all wheels inspected and 
the disposition made of them. 

Rejections 

14. Individual wheels will be considered to have failed and will not 
be accepted or further considered, which. 

First. Do not conform to standard design and measurement. 

Second. Are under or over weight. 

Third. Have the physical defects described in Section 6. 

15. Each 103 wheels submitted for test will be considered to have 
failed and will not be accepted or considered further, if. 

First. The test wheels do not conform to Section 7, especially as to 
limits of white iron in the throat and tread and around chaplets. 



Standard Specifications for Locomotive Cylinders 355 

Second. One of the test wheels does not stand the drop test as de- 
scribed in Section 11. 

Third. Both of the two test wheels do not stand the thermal test as 
described in Section 12. 

Standard Specifications for Locomotive Cylinders 

Process of Manufacture 
Locomotive cylinders shall be made from a good quality of close-grained 
gray iron cast in a dry sand mould. 

Chemical Properties 
Drillings taken from test pieces cast as hereafter mentioned shall 
conforrn to the following limits in chemical composition: 

Silicon from 1.25 to 1.75 per cent 

Phosphorus not over o . 90 per cent 

Sulphur not over o. 10 per cent 

Physical Properties 

The minimum physical qualities for cylinder iron shall be as follows: 

The "Arbitration Test Bar," iH inches in diameter, with supports 

12 inches apart, shall have a transverse strength not less than 3000 

pounds, centrally appUed, and a deflection not less than o.io of an inch. 

Test Pieces and Method of Testing 

The standard test-bar shall be iH inches in diameter, about 14 inches 
long, cast on end in dry sand. The drillings for analysis shall be taken 
from this test piece, but in case of rejection the manufacturer shall have 
the option of analyzing drilhngs from the bore of the cylinder, upon 
which analysis the acceptance or rejection of the cylinder shall be based. 

One test piece for each cylinder shall be required. 

Character of Castings 

Castings shall be smooth, well cleaned, free from blow-holes, shrinkage 
cracks or other defects, and must finish to blue-print size. 

Each cyhnder shall have cast on each side of saddle, the manufacturer's 
mark, serial number, date made and mark showing order number. 

Inspector 

The inspector representing the purchaser shall have all reasonable 

facihties afforded to him by the manufacturer to satisfy himself that the 

finished material is furnished in accordance with these specifications. 

All tests and inspections shall be made at the place of the manufacturer. 



356 Standard Specifications for Cast Iron Pipe 

Standard Specifications for Cast-Iron Pipe and 
Special Castings 

Description of Pipes 

The pipes shall be made with hub and spigot joints, and shall accurately 
conform to the dimensions given in tablss Nos. I and II. They shall be 
straight and shall be true circles in section, with their inner and outer 
surfaces concentric, and shall be of the specified dimensions in outside 
diameter. They shall be at least 12 feet in length, exclusive of socket. 
For pipes of each size from 4-inch to 24-inch, inclusive, there shall be two 
standards of outside diameter, and for pipes from 30-inch to 60-inch, 
inclusive, there shall be four standards of outside diameter, as shown by 
table No. II. 

All pipes having the same outside diameter shall have the same inside 
diameter at both ends. The inside diameter of the lighter pipes of each 
standard outside diameter shall be gradually increased for a distance of 
about 6 inches from each end of the pipe so as to obtain the required 
standard thickness and weight for each size and class of pipe. 

Pipes whose standard thickness and weight are intermediate between 
the classes in table No. II shall be made of the same outside diameter as 
the next heavier class. Pipes whose standard thickness and weight are 
less than shown by table No. II shall be made of the same outside diam- 
eter as the class A pipes, and pipes whose thickness and weight are more 
than shown by table No. II shall be made of the same outside diameter 
as the class D pipes. 

For 4-inch to 12-inch pipes, inclusive, one class of special castings 
shall be furnished, made from class D pattern. Those having spigot 
ends shall have outside diameters of spigot ends midway between the 
two standards of outside diameters as shown by table No. II, and shall be 
tapered back for a distance of 6 inches. For 14-inch to 24-inch pipes, 
inclusive, two classes of special castings shall be furnished, class B spe- 
cial castings with classes A and B pipes, and class D special castings 
with classes C and D pipes, the former to be stamped "AB" and the 
latter to be stamped "CD." For 30-inch to 60-inch pipes, inclusive, 
four classes of special castings shall be furnished, one for each class of 
pipe, and shall be stamped with the letter of the class to which they 
belong. 

Allowable Variation in Diameter of Pipes and Sockets 
Especial care shall be taken to have the sockets of the required size. 
The sockets and spigots will be tested by circular gauges, and no pipe will 
be received which is defective in joint room from any cause. The diam- 
eters of the sockets and the outside diameters of the bead ends of the 



Special Castings 357 

pipes shall not vary from the standard dimensions by more than 0.06 
of an inch for pipes 16 inches or less in diameter; 0.08 of an inch for 
18-inch, 20-inch and 24-inch pipes; o.io of an inch for 30-inch, 36-inch 
and 42-inch pipes; 0.12 of an inch for 48-inch, and 0.15 of an inch for 
54-inch and 60-inch pipes. 

Allowable Variation in Thickness 

For pipes whose standard thickness is less than i inch, the thickness of 
metal in the body of the pipe shall not be more than 0.08 of an inch less 
than the standard thickness, and for pipes whose standard thickness is 
I inch or more, the variation shall not exceed o.io of an inch, except that 
for spaces not exceeding 8 inches in length in any direction, variations 
from the standard thickness of 0.02 of an inch in excess of the allowance 
above given shall be permitted. 

For special castings of standard patterns a variation of 50 per cent 
greater than allowed for straight pipe shall be permitted. 

Defective Spigots may he Cut 

Defective spigot ends on pipes 12 inches or more in diameter may be 
cut off in a lathe and a half-round wrought-iron band shrunk into a 
groove cut in the end of the pipe. Not more than 1 2 per cent of the total 
number of accepted pipes of each size shall be cut and banded, and no 
pipe shall be banded which is less than 11 feet in length, exclusive of the 
socket. 

In case the length of a pipe differs from 12 feet, the standard weight 
of the pipe given in table No. II shall be modified in accordance therewith. 

Special Castings 

All special castings shall be made in accordance with the cuts and the 
dimensions given in the table forming a part of these specifications. 

The diameters of the sockets and the external diameters of the bead 
ends of the special castings shall not vary from the standard dimensions 
by more than 0.12 of an inch for castings 16 inches or less in diameter; 
0.15 of an inch for 18-inch, 20-Inch and 24-inch castings; 0.20 of an inch 
for 30-inch, 36-inch and 42-inch castings; and 0.24 of an inch for 48- 
inch, 54-inch and 60-inch castings. These variations apply only to 
special castings made from standard patterns. 

The flanges on all manhole castings and manhole covers shall be faced 
true and smooth, and drilled to receive bolts of the sizes given in the 
tables. The manufacturer shall furnish and deUver all bolts for bolting 
on the manhole covers, the bolts to be of the sizes shown on plans and 
made of the best quality of mild steel, with hexagonal heads and nuts 
and sound, well-fitting threads. 



3S8 



Standard Specifications for Cast Iron Pipe 



Table No. I. — General Dimensions or Pipes 




K PipelZ'-O" '>i 

Fig. I02. 



Nom- 




Actual 


Diameter of 
sockets 


Depth of 
sockets 








inal 
diam., 


Classes 


outside 
diam., 










A 


B 




Pipe, 
inches 


Special 


Pipe, 
inches 


Special 


C 


inches 




inches 


castings, 
inches 


castings, 
inches 








4 


A-B 


4.80 


5.60 


5.70 


3.50 


4.00 


1.5 


1.30 


.65 


4 


C-D 


500 


5.80 


5.70 


3.50 


4.00 


1.5 


1.30 


.65 


6 


A-B 


6.90 


7.70 


7.80 


3.50 


4 00 


1.5 


1.40 


.70 


6 


C-D 


7.10 


7.90 


7.80 


3.50 


4.00 


1.5 


1.40 


.70 


8 




9.05 


9.85 


10.00 


4.00 


4.00 


1.5 


1.50 


75 


8 


'c-D 


9.30 


10.10 


10.00 


4.00 


4.00 


1.5 


1.50 


.75 


lo 


A-B 


II. 10 


11.90 


12.10 


4.00 


4.00 


1.5 


1.50 


.75 


lO 


C-D 


11.40 


12.20 


12.10 


4. CO 


4.00 


1.5 


1.60 


.80 


12 


A-B 


13.20 


14.00 


14.20 


4.00 


4.00 


1.5 


1.60 


.80 


12 


C-D 


13.50 


14.30 


14.20 


4.00 


4.00 


1. 5 


1.70 


.85 


14 


A-B 


15.30 


16.10 


16.10 


4.00 


4.00 


1. 5 


1.70 


.85 


14 


C-D 


15.6s 


16.45 


16.45 


4.00 


4.00 


1.5 


1.80 


.90 


i6 


A-B 


17.40 


18.40 


18.40 


4.00 


4.00 


1. 75 


1.80 


.90 


i6 


C- 


17.80 


18.80 


18.80 


4.00 


4.00 


1.75 


1.90 


1. 00 


i8 


A-B 


19.50 


20.50 


20.50 


4.00 


4.00 


1.75 


1.90 


• 95 


i8 


C-D 


19.92 


20.92 


20.92 


4.00 


4.00 


1.75 


2.10 


1.05 


20 


A-B 


21.60 


22.60 


22.60 


4.00 


4.00 


1. 75 


2.00 


x.oo 


20 


C-D 


22.06 


23.06 


23.06 


4.00 


4.00 


1.75 


2.30 


1. 15 


24 


A-B 


25.80 


26.80 


26.80 


4.00 


4.00 


2.00 


2.10 


1.05 


24 


C-D 


26.32 


27.32 


27.32 


4.00 


4.00 


2.00 


2.50 


1. 25 


30 


A 


31.74 


32.74 


32.74 


4.50 


4.50 


2.00 


2.50 


LIS 


30 


B 


32.00 


33.00 


33.00 


4.50 


4.50 


2.00 


2.30 


I. IS 


30 


C 


32.40 


33.40 


33.40 


4.50 


4.50 


2.00 


2.60 


1.32 


30 


D 


32.74 


33.74 


33.74 


4.50 


4.50 


2.00 


3.00 


1.50 


36 


A 


37.96 


38.96 


38.96 


4.50 


4.50 


2.00 


2.50 


1. 25 


36 


B 


38.30 


39.30 


39.30 


4.50 


4.50 


2.00 


2.80 


1.40 


36 


C 


38.70 


39.70 


39.70 


4.50 


4.50 


2.00 


3.10 


1.60 


36 


D 


39.16 


40.16 


40.16 


4.50 


4.50 


2.00 


3.40 


1.80 


42 


A 


44.20 


45.20 


45. 20 


5.00 


5.00 


2.00 


2.80 


1.40 


42 


B 


44.50 


45.50 


45.50 


5.00 


5.00 


2.00 


3.00 


I. SO 


42 


C 


45.10 


46.10 


46.10 


5.00 


5.00 


2.00 


3.40 


1. 75 


42 


D 


45.58 


46.58 


46.58 


5.00 


5.00 


2.00 


3.80 


1.95 


48 


A 


50.50 


51.50 


51.50 


5.00 


5.00 


2.00 


3.00 


1.50 


48 


B 


50.80 


51.80 


51.80 


5.00 


5.00 


2.00 


3.30 


1. 6s 


48 


C 


51.40 


52.40 


52.40 


5.00 


5.00 


2.00 


3.80 


1.95 


48 


D 


51.98 


52.98 


52.98 


5.00 


500 


2.00 


4.20 


2.20 


54 


A 


56.66 


57.66 


57.66 


5.50 


5.50 


2.25 


3.20 


1.60 


54 


B 


57.10 


58.10 


58.10 


5.50 


5.50 


2.25 


3.60 


1.80 


54 


C 


57.80 


58.80 


58.80 


5.50 


5.50 


2.25 


4.00 


2.15 


54 


D 


58.40 


59.40 


59.40 


5.50 


5.50 


2.25 


4.40 


2.45 


60 


A 


62.80 


63.80 


63.80 


5.50 


5.50 


2.25 


3.40 


1.70 


60 


B 


63.40 


64.40 


64.40 


5.50 


5.50 


2.25 


3.70 


1.90 


60 


C 


64.20 


65.20 


65.20 


5.50 


5.50 


2.25 


4.20 


2.25 


60 


D 


64.82 


65.82 


65.82 


5.50 


5.50 


2.25 


4.70 


2.60 



Standard Specifications for Cast Iron Pipe 



359 



Table No. II. — Standard Thicknesses and Weights of 
Cast Iron Pipe 







Class A 






Class B 




Nominal 


ICO ft. head. 43 lbs. 


pressure 


200 ft. head. 86 lbs. 


pressure 


inside 

diameter, 

inches 














Thickness, 
inches 


Weight per 


Thickness, 
inches 


Weight per 




Foot 


Length 


Foot 


Length 


4 


• 42 


20.0 


240 


.45 


21.7 


260 


6 


.44 


30.8 


370 


.48 


33.3 


400 


8 


-.46 


42.9 


515 


.51 


47-5 


570 


lO 


.50 


57.1 


685 


.57 


63.8 


765 


12 


.54 


72.5 


870 


.62 


82.1 


985 


14 


.57 


89.6 


1.075 


.66 


102.5 


1,230 


i6 


.60 


108.3 


1,300 


.70 


125.0 


1,500 


i8 


.64 


129.2 


1,550 


.75 


150.0 


1,800 


20 


.67 


150 


1,800 


.80 


175.0 


2,100 


24 


.76 


204.2 


2,450 


89 


233.3 


2,800 


30 


.88 


291.7 


3,500 


1.03 


333.3 


4,000 


36 


■ 99 


391.7 


4,700 


1. 15 


454.2 


5,450 


42 


I. ID 


512. 5 


6,150 


1.28 


591.7 


7,100 


48 


1.26 


666.7 


8,000 


1.42 


750.0 


9,000 


54 


1.35 


800.0 


9,600 


1.55 


933.3 


11,200 


6o 


1.39 


916.7 


11,000 


1.67 


1,104.2 


13,250 






Class C 






Class D 




Nominal 


300 ft. he£ 


id. 130 lbs. 


pressure 


400 ft. he 


ad. 173 lbs 


. pressure 


inside 

diameter, 

inches 














Thickness, 
inches 


Weig 


ht per 


Thickness, 
inches 


Weig 


ht per 




Foot 


Length 


Foot 


Length 


4 


.48 


23.3 


280 


.52 


25.0 


300 


6 




51 


35.8 


430 


.55 


38.3 


460 


8 




56 


52.1 


625 


.60 


55.8 


670 


lO 




62 


70.8 


850 


.68 


76.7 


920 


12 




68 


91.7 


1,100 


.75 


100. 


1,200 


14 




74 


116. 7 


1,400 


.82 


129.2 


1,550 


l6 




80 


143.8 


1,725 


.89 


158.3 


1,900 


i8 




87 


175.0 


2,100 


.96 


191. 7 


2,300 


20 




92 


208.3 


2,500 


1.03 


229.2 


2,750 


24 




04 


279.2 


3,350 


1. 16 


306.7 


3,680 


30 




20 


400.0 


4,800 


1.37 


450.0 


5.400 


36 




36 


545.8 


6,550 


1.58 


625.0 


7.500 


42 




54 


716.7 


8,600 


1.78 


825.0 


9.900 


48 




71 


908.3 


10,900 


1.96 


1050.0 


12,600 


54 




90 


1,141.7 


13,700 


2.23 


1341.7 


16,100 


6o 


2 


00 


1,341.7 


16,100 


2.38 


1583.3 


19,000 



The above weights are for 12-feet laying lengths and standard sockets; propor- 
tionate allowance to be made for any variation therefrom. 



360 Standard Specifications for Cast Iron Pipe 

Marking 
Every pipe and special casting shall have distinctly cast upon it the 
initials of the maker's name. When cast especially to order, each pipe 
and special casting larger than 4-inch may also have cast upon it figures 
showing the year in which it was cast and a number signifying the order 
in point of time in which it was cast, the figures denoting the year being 
above and the number below, thus: 

1901 1901 1901 

I 2 3 

etc., also any initials, not exceeding four, which may be required by the 
purchaser. The letters and figures shall be cast on the outside and shall 
be not less than 2 inches in length and % of an inch in relief for pipes 
8 inches in diameter and larger. For smaller sizes of pipes the letters 
may be i inch in length. The weight and the class letter shall be con- 
spicuously painted in white on the inside of each pipe and special casting 
after the coating has become hard. 

Allowable Percentage of Variation in Weight 
No pipe shall be accepted the weight of which shall be less than the 
standard weight by more than 5 per cent for pipes 16 inches or less in 
diameter, and 4 per cent for pipes more than 16 inches in diameter, and 
no excess above the standard weight of more than the given percentages 
for the several sizes shall be paid for. The total weight to be paid for 
shall not exceed, for each size and class of pipe received, the sum of the 
standard weights of the same number of pieces of the given size and class 
by more than 2 per cent. 

No special casting shall be accepted the weight of which shall be less 
than the standard weight by more than 10 per cent for pipes 12 inches 
or less in diameter, and 8 per cent for larger sizes, except that curves, 
Y pieces and breeches pipe may be 12 per cent below the standard weight, 
and no excess above the standard weight of more than the above per- 
centages for the several sizes will be paid for. These variations apply 
only to castings made from the standard patterns. 

Quality of Iron 
All pipes and special castings shall be made of cast iron of good quality 
and of such character as shall make the metal of the castings strong, 
tough and of even grain, and soft enough to satisfactorily admit of 
drilling and cutting. The metal shall be made without any admixtiu"e 
of cinder iron or other inferior metal, and shall be remelted in a cupola 
or air furnace. 



Coating 361 

Tests of Material 
Specimen bars of the metal used, each being 26 inches long by 2 inches 
wide and i inch thick, shall be made without charge as often as the 
engineer may direct, and, in default of definite instructions, the con- 
tractor shall make and test at least one bar from each heat or run of 
metal. The bars, when placed flatwise upon supports 24 inches apart 
and loaded in the center, shall for pipes 12 inches or less in diameter 
support a load of 1900 pounds and show a deflection of not less than 0.30 
of an inch before breaking, and for pipes of sizes larger than 12 inches 
shall support a load of 2000 pounds and show a deflection of not less than 
0.32 of an inch. The contractor shall have the right to make and break 
three bars from each heat or run of metal, and the test shall be based upon 
the average results of the three bars. Should the dimensions of the bars 
differ from those above given, a proper allowance therefor shall be made 
in the results of the tests. 

Casting of Pipes 

The straight pipes shall be cast in dry sand moulds in a vertical position. 
Pipes 16 inches or less in diameter shall be cast with the hub end up or 
down, as specified in the proposal. Pipes 18 inches or more in diameter 
shall be cast with the hub end down. 

The pipes shall not be stripped or taken from the pit while showing 
color of heat, but shall be left in the flasks for a sufficient length of time 
to prevent unequal contraction by subsequent exposure. 

Quality of Castings 
The pipes and special castings shall be smooth, free from scales, lumps, 
blisters, sand holes and defects of every nature which unfit them for the 
use for which they are intended. No plugging or filUng will be allowed. 

Cleaning and Inspection 
All pipes and special castings shall be thoroughly cleaned and sub- 
jected to a careful hammer inspection. No casting shall be coated unless 
entirely clean and free from rust, and approved in these respects by the 
engineer immediately before being dipped. 

Coating 

Every pipe and special casting shall be coated inside and out with coal- 
tar pitch varnish. The varnish shall be made from coal tar. To this 
material sufiicient oil may be added to make a smooth coating, tough and 
tenacious when cold, and not brittle nor with any tendency to scale off. 

Each casting shall be heated to a temperature of 300° F., immediately 
before it is dipped, and shall possess not less than this temperature at the 



362 



Standard Specifications for Cast Iron Pipe 



time it is put in the vat. The ovens in which the pipes are heated shall 
be so arranged that all portions of the pipe shall be heated to an even 
temperature. Each casting shall remain in the bath at least five minutes. 

The varnish shall be heated to a temperature of 300° F. (or less if the 
engineer shall so order), and shall be maintained at this temperature 
during the time the casting is immersed. 

Fresh pitch and oil shall be added when necessary to keep the mixture 
at the proper consistency, and the vat shall be emptied of its contents 
and refilled with fresh pitch when deemed, necessary by the engineer. 
After being coated the pipes shall be carefully drained of the surplus 
varnish. Any pipe or special casting that is to be recoated shall first be 
thoroughly scraped and cleaned. 

Hydrostatic Test 

When the coating has become hard, the straight pipes shall be sub- 
jected to a proof by hydrostatic pressure, and, if required by the engineer, 
they shall also be subjected to a hammer test under this pressure. 

The pressures to which the different sizes and classes of pipes shall be 
subjected are as follows: 



Classes 


20-inch diam- 
eter and larger, 
pounds per 
square inch 


Less than 
20-inch diam- 
eter, pounds 
per square inch 


Class A pipe 

Class B pipe 

Class C pipe 

Class Dpipe 


ISO 
200 
250 
300 


300 
300 
300 
300 



Weighing 
The pipes and special castings shall be weighed for payment under the 
supervision of the engineer after the application of the coal-tar pitch 
varnish. If desired by the engineer, the pipes and special castings shall 
be weighed after their delivery and the weights so ascertained shall be 
used in the final settlement, provided such weighing is done by a legalized 
weighmaster. Bids shall be submitted and a final settlement made upon 
the basis of a ton of 2000 pounds. 

Contractor to Furnish Men and Materials 
The contractor shall provide all tools, testing machines, materials and 
men necessary for the required testing, inspection and weighing at the 
foundry, of the pipes and special castings; and, should the purchaser have 



Engineer or Inspector 363 

no inspector at the works, the contractor shall, if required by the engineer, 
furnish a sworn statement that all of the tests have been made as specified, 
this statement to contain the results of the tests upon the test bars. 

Power of Engineer to Inspect 

The engineer shall be at Uberty at all times to inspect the material at 
the foundry, and the moulding, casting and coating of the pipes and special 
castings. The forms, sizes, uniformity and conditions of all pipes and 
other castings herein referred to shall be subject to his inspection and 
approval, and he may reject, without proving, any pipes or other casting 
which is not in conformity with the specifications or drawings. 

Inspector to Report 

The inspector at the foundry shall report daily to the foundry office all 
pipes and special castings rejected, with the causes for rejection. 

Castings to he Delivered Sound and Perfect 

All the pipes and other castings must be delivered in all respects sound 
and conformable to these specifications. The inspection shall not reheve 
the contractor of any of his obligations in this respect, and any defective 
pipe or other castings which may have passed the engineer at the works 
or elsewhere shall be at all times liable to rejection when discovered imtil 
the final completion and adjustment of the contract, provided, however, 
that the contractor shall not be held liable for pipes or special castings 
found to be cracked after they have been accepted at the agreed point of 
dehvery. Care shall be taken in handUng the pipes not to injure the 
coating, and no pipes or other material of any kind shall be placed in the 
pipes during transportation or at any time after they receive the coating. 

Definition of the Word ^^ Engineer" 

Wherever the word "engineer" is used herein it shall be understood 
to refer to the engineer or inspector acting for the purchaser and to his 
properly authorized agents, limited by the particular duties intrusted 
to them. 



364 Standard Specifications for Cast Iron Pipe 

Volume and Weight of Piled, Bell and Spigot Cast Iron Pipe 



Size of 


Head 


Thick- 


Weight 


No. of 
pipes in 


Cubic 
feet in 


No. of 


Pounds 


Cubic 


pipe, 


in 


ness of 


of one 


one ton 


one ton 


pipes in 


of pipe 


feet in 


inches 


feet 


metal, 
inches 


pipe in 
pounds 


of 2240 
pounds 


of 2240 
pounds 


40 cubic 

feet 


in 40 
cubic feet 


one 
pipe 


3 


100 


-.38 


167 


I3^4l 


21.414 


24.935 


4164. 121 


1.604 


3 


200 


.42 


18S 


12. II 


19.796 


24.46s 


4523.320 


1.63s 


3 


300 


• 45 


200 


11.20 


18.961 


23.626 


4724.224 


1.693 


3 


400 


• 45 


200 


11.20 


18.961 


23.626 


4724.224 


1.693 


4 


100 


.40 


230 


9.74 


23.646 


16.479 


3787.720 


2.428 


4 


200 


.42 


243 


9.26 


22.953 


16.135 


3920.034 


2.479 


4 


300 


• 45 


260 


8.61 


22.873 


15.754 


4004.480 


2.539 


4 


400 


• 47 


265 


8.45 


21.823 


15.491 


4104.372 


2.S82 


5 


100 _ 


• 42 


29s 


7.59 


26.S37 


11.433 


3376.136 


3.49s 


5 


200 


• 45 


31S 


7. II 


25.356 


11.222 


3534.332 


3.565 


5 


300 


.48 


338 


6.63 


24.13s 


10.983 


3712.000 


3.642 


5 


400 


• 51 


355 


6.31 


23.503 


10.738 


3811.172 


3.725 


6 


100 


• 43 


364 


6. IS 


28.82s 


8.359 


3008.000 


4.684 


6 


200 


• 47 


393 


5.70 


27.28s 


8.356 


3283.240 


4.787 


6 


300 


• 51 


426 


S.2S 


25^764 


8.177 


3477.224 


4.900 


6 


400 


.54 


445 


5. 03 


25.114 


8.017 


3567.092 


4.990 


8 


100 


• 47 


513 


4.36 


33.425 


5.224 


2680.164 


7.656 


8 


200 


.51 


567 


3.95 


30.833 


5. 118 


2906.196 


7.804 


8 


300 


• 56 


624 


3.59 


28.666 


5.009 


3129.392 


7.98s 


8 


400 


.61 


66s 


3.37 


27.456 


4.906 


3262.730 


8.152 


10 


100 


.50 


685 


3.27 


37.400 


3.454 


2366.256 


11.579 


10 


200 


.56 


765 


2.93 


34-676 


3.388 


2587.484 


11.826 


10 


300 


.62 


852 


2.63 


31.800 


3.317 


2826.248 


12.058 


10 


400 


.68 


920 


2.43 


30.266 


3.216 


2959.172 


12.435 


12 


100 


.53 


870 


2.57 


41.230 


2.497 


2172.492 


16.018 


12 


200 


.60 


985 


2.27 


37-218 


2.444 


2407.236 


X6.367 


12 


300 


.68 


IIIO 


2.02 


33.858 


2.384 


2646.288 


16.778 


12 


400 


• 75 


1210 


1.98 


34.839 


2.159 


2612.892 


17.549 


14 


100 


.56 


1074 


2.08 


44-310 


1.882 


2021 . 388 


21 . 252 


14 


200 


.65 


1229 


1.82 


39-798 


1. 831 


2250.592 


21.843 


14 


300 


• 73 


1399 


1.60 


35.699 


1.794 


2509.568 


22.298 


14 


400 


.82 


1540 


1.45 


33.242 


1.757 


2969.184 


22.847 


16 


100 


.60 


1293 


1.73 


47.325 


1.464 


1893.864 


27.308 


16 


200 


•69 


1496 


1.50 


41-829 


1.434 


2145.788 


27.886 


16 


300 


.79 


1723 


1.30 


37.095 


1. 401 


2415.256 


28.535 


16 


400 


.89 


1900 


1. 18 


36.020 


1. 316 


2490.308 


30.578 


18 


100 


• 63 


1532 


1.46 


48.274 


1. 211 


1855.876 


33019 


18 


200 


74 


I7b8 


1.28 


44.456 


1. 157 


2068.864 


34.569 


18 


300 


.85 


2065 


1.08 


38.572 


1. 124 


2321 . 284 


35.583 


18 


400 


.96 


2300 


.974 


35.441 


T.IOO 


2532.076 


36.338 



Volume and Weight of Piled, Bell and Spigot Cast Iron Pipe 365 



Volume and Weight of Piled, Bell and Spigot Cast 
Iron Pipe {Continued) 



Size of 


Head 


Thick- 


Weight 


No. of 
pipes in 


Cubic 
feet in 


No. of 


Pounds 


Cubic 


pipe, 
inches 


in 

feet 


ness of 
metal, 
inches 


of one 
pipe in 
pounds 


one ton 
of 2240 
pounds 


one ton 
of 2240 
pounds 


pipes in 

40 cubic 

feet 


of pipe 

in 40 

cubic feet 


feet in 
one 
pipe 


20 


100 


.66 


1,788 


1.28 


53.874 


.945 • 


1778.040 


41.893 


20 


200 


.78 


2,104 


1.06 


45.596 


.938 


1963.836 


42.854 


20 


300 


• 91 


2,444 


.916 


39900 


.918 


2240.272 


43.559 


20 


400 


■03 


2,740 


.814 


36.508 


.891 


2443.188 


44.850 


24 


100 


.75 


2,407 


.931 


55.122 


.679 


1626.132 


59.207 


24. 


200 


.87 


2,803 


.799 


49.463 


.646 


1811.112 


61.906 


24 


300 


1.02 


3,299 


.679 


43-122 


.630 


2080.876 


63.41S 


24 


400 


1. 16 


3,680 


.600 


38.783 


.619 


2277.256 


64.639 


30 


100 


.87 


3.482 


.649 


59.733 


.434 


1513.268 


92.039 


30 


200 


1. 01 


4,027 


.556 


52.760 


.421 


1697.492 


94.892 


30 


300 


1. 19 


4,783 


.468 


45.550 


.411 


1965.660 


97.337 


30 


400 


1.37 


5,420 


.413 


41.047 


.402 


2181.364 


99.387 


36 


100 


.98 


4,699 


.476 


63.567 


.299 


1407.388 


133.544 


36 


200 


1. 14 


5,460 


.410 


55.586 


.295 


1610.884 


135.577 


36 


300 


1.36 


6,543 


.342 


47.019 


.291 


1903.636 


137.484 


36 


400 


1.58 


7,490 


.300 


42.566 


.282 


2111.516 


141.888 


40 


100 


1.09 


5,807 


.386 


63.591 


.242 


1409.936 


164.745 


40 


200 


1.23 


6,525 


.343 


56.997 


.240 


1570.636 


166.174 


40 


300 


1.48 


7,858 


.285 


48.909 


.233 


1831.588 


171. 610 


40 


400 


1.72 


9,050 


.247 


43.413 


.227 


2059.372 


175.763 


42 


100 


1. 10 


6,147 


.364 


66.117 


.225 


1353.628 


181.640 


42 


200 


1.28 


7,100 


.315 


58.179 


.216 


1537.664 


184.695 


42 


300 


1.54 


8,563 


.258 


48.802 


.211 


1810.768 


189.157 


42 


400 


1.79 


9,890 


.248 


48.002 


.206 


2043.812 


193.559 


48 


100 


1.25 


7,982 


.281 


65.246 


.171 


1370.164 


233.023 


48 


200 


1. 41 


8,946 


.250 


59.800 


.167 


1496.000 


239.200 


48 


300 


1. 71 


10,857 


.206 


50.862 


.166 


1758.940 


246.903 


48 


400 


1.99 


12,550 


.179 


44.767 


.163 


2007.856 


250.097 


60 


100 


1.40 


11,000 


.203 


74.817 


.108 


1193.836 


368.559 


60 


200 


1.68 


13,260 ■ 


.169 


63.188 


.107 


1418.568 


373.897 


60 


300 


2.05 


16,040 


.139 


52.903 


.105 


1685 . 760 


380.599 


60 


400 


2.41 


18,970 


.118 


46.253 


.102 


1938.820 


391.978 




Fig. 103. — Pile of 100 Pipe. 



366 



Standard Specifications for Cast Iron Pipe 



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<Ci lO r^vO 00 t^ O>00 



io\ ro "O"^ lO c« t^ 



1/) <M M 00 t~ fO 

w M ro N CO f^ 



ON •* U5\ <N 
rH O) M M 

T}- (^ to ■<d- 



M O —xoo »-N 
\0 ir> t~ir) " 



t^ vfjto \!;^ vo 



) vo cm:^ m ( 



O. M M M 



IT) NpO M NpOO ^ CS 

M inN o^ inxto "3N 1^ 



^00 X^' 

^ M ,-1 0> 

M 00 f^O> 

(N M N M 



rt t^ eoN CT> _i ej 



«NvO c§^ O 



;5l, 



N V- O N- 



t^ rO 0» lo 



Oi CNVO lON 



fj "ON o 



rJSOO —N O 



■-iN O •-*o <J> ^po O ^ < 
^ ir^ cc\ <N co\ M wvo 
<o ■* r- ly^ 00 o oiy 



OO M 



in-soo s?' q> 
"to O 



O^ rt O ^x ic 






O V- t^ N-- IN 



s:a 



Nfovo vmoo 
t~xio tis (N 
TT (M lo r<7 



M V* lO vjvo 

t> rtX Tl- wN M 

^ 00 lO CJi^O 



;:§^5 



I o t^ M a> ( 



N lo ro 



vo vr' "* sr< ro \- 0> 



c%N tT 



vo fC f^ •» 00 iQ CMC 



6 ^ M M 
HlO M l> 



L-y- IN >oN 1 
r-- M a> I 



spo Tf ^50 cri 

«N 0» «\ (M 
M ro ro IT) 



lOVO 



-^ ■<«■ SOOO 
nN (N cSnoo 
•^ M to CM 



NfC M spOO ^ lj> S50 fO 

CON lO -•N M rH\ 1> T->S -^ 



ro i?> lo I 



0» M M M 



V- O N- l> 

U5N M iO\ r) 
M ro fO ■* 



s.'S is :S'S sS'i-^;5:S- 

rtiN lOiN'OrOt-rOoO'^aiiO 



'oo 



Njl<VO 

^\ M 

M M 



CO O^ CO ■ 
ro M rf I 



Q O M 

VO M t>> 

t^ ro 00 ■* 0> ■* 






spO NpO M 

r-.\ 0> "N ro 

i> M a» o 



vfO SCO 

CSs t> «v O^ 

CI t^ « <N 

ro M ^ (N 



dfsM irisrOiSNi/jioxi/) 
imoOm rOr-iOOM ro 
ION <£>rO t^rOOO'T 



IN O IN M 
1-0 M Tt IN 



lO N VO ro r~ ro 00 



ION )2n 

0> rt t- CO '^ 
^ O Oi <N 0> 



NfO SfO 

iriN t^ io\ M 

M "* IN a> 

ro M -^ M 



lox lo CON o^ CON ro co\ t~ 
iMrOrfr^--<NMVO 
lONvOiN t^roooro 



to Nr-' 

c?s M 2 IN 

rt t- O M 

Oi 00 M ri- 



h-rt 


.b-n 


. c 


- a 


<u 3 


m ;j 


•^g 


•ao 






.St3 



gs 



fS^ p:^ p:^ 



^ : ^ _ 

^01 Mtn ^w 5^03 

.Stj .^'d .S'O .StJ 

(U;3 OJrJ dJW (Ur^ 

.2 o .2 o .N o .S o 

g^- ^^ g+^- g+i' 

i^M ^ M i^ M ^ M 

^1 ^1 i«l ^'^ 

PL,^ CL,^ Ph^ Oh^ 



cjq c 's CJ2 _c 






CI 

3 



w P< 



- G 
.2 o 

to Q< 



5 a 



"m P- "w 



.G-O 
- G 

•2 9 

M O. 



fri i-i. C r! 



Ph^ cw^ eu^ 



i^ M ^ M 

III! 



^.S- g.S- g.& ^.& g.& ^.& ^.2" g.& ^.& ^.2< g.& ^.& g.S- ^.S- g.S< §.2- S.S- 
■'fdi -tCm "rPH -vP^ "tPh -vcih -vPh -jcw -rctn "rO, -jPn -vPh -vOi "rfii -7(1, -jfii -vPh 

MWMMMWNNWrO 



Pattern Size and Weight of Cast Iron Pipe 



367 



10 00 00 O M 



to ^90 ro ^ O 
■<a-oo <o >-> 



V*' I> x* t^ 
to ■* 00 t^ 



m-^VO m^ 10 M'^ t S« ro ttf^ O 
- CTi- w - rO'-'^CTi-.tO 
CsrO'^t^tOO C^CTlOOCTl 
Mro N(*5 !Nt ro-* roio 



-N M r-x ro — ^ 10 



10 <N t^ ■^ O 



toroooto OOiMro -^tO tO a> <N 00 00 
MO) Mcs PiM (NroMrOMrr;rO'*!~oi 



O rO 1-1 irj N to "^ 



VO CO 00 "O 



oro 1-iu^ <Nto -^cnto 



MM M (M M CM CM 



inx <N lox (N irSN M ^ o MX o> 

(NM -^^tOt^CMVOOO-* 

CM fO N W IN ro (^ ■* ro >r> 



00 '^ O r~ 



■00 X— to N-. CM -^ <0 —xto 
s rO ctX CM cs~- >-< inx t^ ^ -^ 



1/5 Tj-OO to M 00 ro 



- 0> x<>' C^ ^^ 0% 
^tO "X T^ wx M 

1^ ^ 



-Jx O O (M M 



spcto Npot^Njao^x-'M X— N s—rovf) 

cox -* rtx M «xoo t^xto t^ fO t-\ O '-'"~^ 

VOOOO^O OiO<Nc» •^Mto^CN 

MN MCM <N(N NM CMCOCMrOfO 



VOtO 



,-.X Ifl OiX M 



l> t~ 00 0% CJl I 



10 X- 0» xoo 00 

^ >ox o n'x !>. 

CM O 10 C-) t~ 

CM <N (N <N (M 



• O <£> 
CT) PJ 



i> r~ 00 00 



:ss 



00 x-tO X" N x-f 

t^ COX Q tOstO ^"x 



^X M ^X I> ^X O) 



X— O X-IO--90CM S—IO 

lox .;j- uix cji P3X to t~x ro 
•^OvtOM <Naiool> 
CM CM IN ro ro ro ro -^ 



SS> SI 



S^:;xv 

C~ t~ 00 c 



^2t.:i^s :s;^ 



Npooo ^pto 
^x 10 lox o 
IN ro •^to 



O^ x^tO x-i" ■* XTf IN X— -^ Npo ro 
. -^ i-x cTi ^x ^ _x ov lox ro mxoo 
ro CM 10 Tf 00 to O CN 00 00 I/; 
CM iNiN CMiN (NrororOrOTT 



I iA> to t- 00 00 o>g> 



^x M ^sx 10 
IN 1^ Tt 10 to t^ 00 



:sg:si 



X— 00 X— 00 X— CJ^ X'* J> sr-i h 

cox O cox Tt cox 00 i-X O lOX ( 

CMIO •>*r~tOOi CMt^OO- 

CM CM CM IN CM M ro (^ ro • 



to to r»oo 



S^tO 
00 0\ 



O M M IN CM 



Tftot>ooa>OM CM 



- Ol -■X IN r-X to 



tJ5^! 



f3 



IN ■* 

10 in 



t-X |> nSO ov 

iM m t~\to 
to to t^ l> 






isx 10 uoxtj 



O^OM MM rO'^vOtooooo Om 



•^ lO to I> CM ■* 

CM CM CM CM r<^ ro 



rt ■* m \ri 



XCO X— 

inx M coxoo 
N CO -H fC 

to to r- t^ 



cox Tl- f~xto 
CftS 2 2 



X— N— V 10 

lox M lox t^ uix M to Tj- 0> X- I> 

„O^M-<rO •* to t^-nXIN 

IDtO t-00 Ov O IN (N Tt-^tOtO <N ro 

MM MM mCM CMIN OJCM CMCM fOCO 



;l^to ^ 






00 00 q> oi 



<tO ^ M 

o o 



, (T) t^X M 

CM M ro 

M CO CO 



spooo ^^ to ^^ ^ 
Kx ro t'"^ "^ t^"x \n 



(N CM CN <N 



.2 o .2 o 

CO p< 03 p. 






lU 3 

.2 o 



.2 o 






CJ- C-w" «-m" c. 



d .i3'T3 .S'u .!:;'d .tJ'd .IS'd -"t) , 

C -a -C -C .G -G -G 

M (Urj (d;3 ds (ua 4)3 4;3 

o .2 o .2 o .2 o N o .2 o .2 o 

p. M P< m P< 'w P< ■(« a 'to P< oi P< 

J G +; G ^- C ^- G +r C ^- G +;■ 

S, fe-S «-f S-B, fe-S, fe-S v-E 

fil "t^'lU "'^ *«! "H'ln ■*^*fn "•^'(Tl +:J'(n 



S'd 
- G 

2 o 
« a 

G+;- 



.a-d 
- G 

.2 o 
w a 



.s-s 

. G 

.2 o 

u Vi 



p:^ ^^ ^^ ^^ ^^ ^^ 






rtll rt'lS '^'i. 

PW^ flH^ (1^^ 



bj) ^ M 

fi;^ (i:^ o;^ II 



'f^oj'fiiU'fiiU'fiiD'fiiiJ'fiiU'f^a)'?, iU'?1«'fliU'il4)'fiaj'5liU'5t<U'?l 

S.& ^.2- ^.S" ^.2< ^.2- g.& g.2- S.2- g.2- g.& g.& ^.& g.2< ^.& g-S- S-S- ^.S- 
veLi -vCLi -rPn -"rC^ -vf^ •■rP^ -tP-i 'rPn -vPh -vPh -vPh -vcw -ypli -vcli -vPh "rf^ -tPh 
c»5^io«t^ooa>o CM ■^tooo o M Ti-ou" 

MMMWMCSCMCMCOC 



368 Standard Specifications for Cast Iron Pipe 



roao 









P0"O tf> tr~ 



SCO 00 N- P) sp^ 1 
«N CTi t^\ t- -N lil 



lov o in\ &. n\ Ti- (~s CT> 
ic lO I>-00 COO 0> M 



::t§,:5:^. 












-.\00 ^x rt -N O -X'O 
w ^ 0000 ir. -- ' " 



t^ IT) rovO o> r~ 



_ VP O -\ iJl --s O "^ 

M ro CN ro N ro 






ro vo rovo 



00 Oi O ro P0<O 



NfO MTi- «■* roi/5 



O^ v<c lo veo o >oNio mx N ic-sio fi s 
(N MM (NrONrONr'5(N'rrroir) i 



J2 • ^ .• .^ 



- c 



jj M 4i M 4J bO 



.aT3 

- a 



,aT3 .S'a .sxi 



p. w P. in 



W ft 



- G 

to 0< 



dJ ;3 



ix! .sts .a-o 






N§ §^s sg gg 






- c -c 
.2 o .E2 o 

P< w O. w p. 



i-S, (LI'S, 






Ph^ Ph^ Ph^ O,^ Ph^ Cl,^ (Ih^ Ph^ P.^ Ph^ P.^ Ph^ P.^ Ph^ Ah^ Ph^ Ph^ 



OQ.oS.uS-OQ.yp.^p.'Jp.yp.^o.^o.yp.^p.'Jp.^a.Up.WQ.'^Q. 
C.S' a-S* C.S* C-S C--^ G-s^ G-i- G-- G-- G-- G-- G-- C-" C-- G-" G-"- C-5« 

••rp^ -tPh -vPh -vPh -rPn -rP^ -vPh -vct, -vp^ -vCu -tPh -tp^ -jPh "tPh -tPh -vi^ -vp^ 



Pattern Size and Weight of Cast Iron Pipe 



369 



Pattern Size and Weight of Cast Iron Pipe, % to ii%2 
Inches Thick 



Thickness, inches 


% 


2542 


1^6 


m2 


5i 


29^2 


1M6 


40-inch 
Pipe 


Pattern size, inches 

Weight, pounds 


42 
3910 


42M6 
407s 


4240 

4440 


42?i6 
4405 

44?i6 
4615 



42H 
4737 
44H 
4790 


425/16 
4903 

44Ma 
496s 


42% 
4903 


42-inch 
Pipe 

48-inch 
Pipe 

60-inch 
Pipe 


Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight, pounds 


5140 
5o7ifl 
5969 



40-inch 

Pipe 
42-inch 

Pipe 
48-inch 

Pipe 
60-inch 

Pipe 



Thickness, inches 



Pattern size, inches. 

Weight, pounds 

Pattern size, inches. 

Weight, pounds 

Pattern size, inches. 
Weight, pounds. ; . . . 
Pattern size, inches. 
Weight, pounds 



^^i2 



42JI6 

5070 

44^6 

5316 

50/2 

6068 



42'A 
5237 
44V^ 
5492 

6267. 



lj'^2 



42?i6 
5404 
449/1 6 

5668 
6467 



iHe 



42H 

.5572 

44% 

5844 

5011/6 

6667 

627/^ 
8282 



I%2 



4211/6 

5740 

44IH6 

6021 

50M 

6867 

621^6 

8532 



Il/i 



42M 
5908 

44% 

6198 

5oiM( 

7067 

63 

8782 



1^2 



421^6 
6077 

44^ Me 

637s 

50^^ 

7268 

63I/6 

9032 



Thickness, inches 



40-inch 

Pipe 
42-inch 

Pipe 
48-inch 

Pipe 
60-inch 

Pipe 



Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight, pounds 

Pattern size, inches 
Weight, pounds 



l3/6 


Ili2 


■ xH 


19^2 


15/ 6 


1IH2 


A2-A 


4215/6 


43 


43M6 


43^/^ 


433/6 


6246 


64IS 


6585 


6755 


6925 


7096 


44^/B 


4415/6 


45 


45/6 


45H 


45M6 


6552 


6730 


6908 


7086 


7264 


7443 


5015/ 6 


51 


51 He 


51^/^ 


51^16 


S1/4 


7469 


7670 


7871 


8073 


827s 


8477 


63>/i 


63^16 


63I/4 


635/6 


63^/^ 


637/6 


9282 


9532 


9782 


10,032 


10,283 


io,S34 



43H 

7267 

45H 

762 

5IM6 

8679 

63!/^ 

10,785 



40-inch 

Pipe 

42-inch 

. Pipe 

48-inch 

Pipe 

60-inch 

Pipe 



Thickness, inches 



Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight , pounds 

Pattern size, inches 
Weight, pounds — . 



Il?^2 



43M6 
7438 
45^16 
7801 

513/8 

8882 
639/6 
11,086 



I7l6 



7610 

453/i 
7980 
51M6 
9083 
635/i 
11,337 



115^2 



43V16 

7782 

45^6 

8160 

51^/ 

9288 

6311/ 6 
11,588 



ll/ 



43^/^ 

7954 

45/2 

8340 

5I?16 

9491 

63% 

11,839 



^^^2 



43?i6 
8127 
459/6 
8520 
5i5/i 

9695 
631^6 

12,091 



iHe 



435/^ 
8300 
45H 
8700 

511/6 

9899 

63^/^ 
12,343 



119^2 



43IH6 

8473 

4511/6 

8881 

513/ 

10,103 

6315/ 6 

12,545 



370 



Standard Specifications for Cast Iron Pipe 



Pattern Size and Weight of Cast Iron Pipe, i^i to 2^2 
Inches Thick 



40-inch 

Pipe 
42-inch 

Pipe 
48-inch 

Pipe 
60-inch 

Pipe 



Thickness, inches 



Pattern 
Weight, 
Pattern 
Weight, 
Pattern 
Weight, 
Pattern 
Weight, 



size, inches 

pounds 

size, inches 

pounds 

size, inches 

pounds 

size, inches 
pounds 



15.^ 


121.^2 


iiHe 


I2-H2 


1% 


43% 


431^6 


43H 


43IM6 


44 


8647 


8821 


8995 


9170 


9345 


45% 


451% 6 


4574 


451^6 


46 


9062 


9243 


9424 


9606 


9788 


5113/16 


sm 


51IM6 


52 


52H6 


10,307 


10,512 


10,717 


10,922 


11,127 


64 


64H6 


641/i 


64% 6 


64H 


12.847 


13.099 


13,357 


13,603 


13,856 



l25'^2 



44H6 
9520 

46Ha 

9970 

52}^ 

11.333 

645/I9 

14.109 



40-inch 

Pipe 
42-inch 

Pipe 
48-inch 

Pipe 
60-inch 

Pipe 



Thickness, inches 



Pattern size, inches 

Weight, pounds 

Pattern size, inches. 

Weight , pounds 

Pattern size, inches. 

Weight, pounds 

Pattern size, inches. 
Weight, pounds. . . . . 



ii^ie 


l2J^2 


iH 


129,62 


iiMe 


44H 


44% 6 


uVi 






9688 


9862 . 


10,048 






46K8 


46% 6 


46H 


46M6 


463,i 


10,152 


10,335 


10,518 


10,700 


10,885 


52M6 


52^/4 


52% 6 


523/i 


52^6 


11,539 


11,745 


11,951 


12,158 


12,365 


64% 


64% 6 


64M6 


64?'i6 


645/i 


14,362 


14,61s 


14,868 


15,121 


15,374 



13^2 



52^ 
12,572 
64IH6 
15,628 



Thickness, inches 


2 


2}i2 


2/16 


23^2 


2H 


40-inch 
Pipe 

42-inch 
Pipe 

48-inch 
Pipe 


Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight, pounds 






52% 6 " 

12,779 

64% 

15,882 


525/^'" 
12,987 
6413/16 
16,136 


521/16' 
13,195 

em 
16,390 


523/4'" 
13,443 
64IM6 
16,644 


521% 6 
13,611 


60-inch 
Pipe 


Pattern size, inches 

Weight, pounds. .... 


65 
16,898 









Thickness, inches 


25/^2 


2H6 


2^2 


2Vi 


2^62 


40-inch 

Pipe 
42-inch 

Pipe 
^'-inch 

Pipe 
60-inch 

Pipe 


Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight, pounds 

Pattern size, inches 

Weight, pounds . ' 






651/6' 
17,152 


65^'" 
17,407 


653/6" 
17,662 


e'sii" 
17,917 


65M6'" 

18,172 









CHAPTER XV 
MECHANICAL ANALYSIS 

While chemical analysis is absolutely necessary for the determination 
of the constituents of iron and the fuels, and is of greatest importance to 
the foundryman as a guide in their purchase, chemists cannot, however, 
as yet predict with certainty the physical properties which will result 
from the mixture of irons possessing identical composition. 

Test bars have shown, that of two irons, precisely the same in their 
chemical constituents, one may exceed the other in tensile strength by 
as much as 50 per cent. No satisfactory explanation of the discrepancy 
has been made. Various suggestions, attributing the cause to the ores, 
changes of temperature in the furnace, to difference in cooling, etc., are 
offered, but the problem is still unsolved. 

Whatever may be the cause of these differences, the foundryman needs 
some means of quickly detecting and correcting them. He should 
have prompt information as to shrinkage, softness and strength of his 
castings. 

During 1885, Mr. Keep made the important discovery that the shrink- 
age of test bars varied inversely as the siUcon content, and that by 
measurement of shrinkage the silicon is practically determined. 

His investigations resulted in pointing out the intimate relations which 
exist between shrinkage and the other properties of cast iron, both 
chemical and physical. Mr. Keep's conclusions as to the importance of 
mechanical analysis are summarized as follows: 

The physical properties of the casting are not wholly dependent upon 
its chemical composition. 

Mechanical analysis measures the physical properties of the iron, 
which are, shrinkage, strength, deflection, set and depth of chill. The 
measure of these properties shows the combined influence of each element 
in the chemical composition, and in addition thereto, it shows the in- 
fluence of fuel and every varying condition attending melting. 

These influences, particularly that of sulphur, are counteracted by the 
use of silicon. 

The measurement of shrinkage tells whether more or less silicon is 
needed to bring the quality of the casting to an accepted standard of 
excellence. 

371 



372 Mechanical Analysis 

Instead of calculating the chemical composition and predicting the 
physical properties, mechanical analysis ascertains the physical proper- 
ties first, and determines from the shrinkage whether more or less silicon 
is required to produce castings of a given standard. Measurement of 
shrinkage is made quickly at a nominal cost and alone gives all necessary 
information. 

It teUs the founder exactly what physical properties his castings have 
and exactly what to do to bring each of those properties to standard. 
By this method a founder can determine whether a low-priced iron is 
suitable for his use. 

Having fixed upon a standard, he can ascertain during the heat 
whether the mixture is of the desired quality, and if necessary can increase 
or decrease the silicon, according as the shrinkage should be reduced or 
increased. 

Mechanical analysis answers all the requirements of the ordinary 
founder. Its simphcity renders the employment of an expert unneces- 
sary. 

Pig iron and coke, having been purchased upon guaranteed analysis, 
an occasional analysis of the castings is only required. 

In a report to The American Society of Mechanical Engineers, Mr. 
Keep presents a Shrinkage Chart and Strength Table, which are given 
below with his directions for using them. 

Shrinkage Chart 

W. J. Keep 

While the tensile tests show an increase of strength with an increase 
of phosphorus, yet the transverse tests seem to show that phosphorus 
reduces strength. This is also general shop experience. 

Sulphur. — There is not in these tests enough imiformity between 
the percentage of sulphur and the strength to show any decided influence, 
but the indication is that sulphur decreases strength. In some cases 
sulphur might add to strength by causing the grain to be closer. 

Manganese. — The percentage is too nearly the same in these series 
to show any influence on strength. 

By comparing strengths and chemical composition of the irons nearest 
ahke, with all chemical elements nearly alike, and no scrap, but with 
quite different strengths, it is very evident that strength is dependent 
upon something outside of the ordinary chemical composition. 

Slow cooHng decreases strength by making the grain of a casting 
coarse and more open. The larger the casting the weaker it become? 
per square inch of section. The weakness is not caused by a decrease 
in combined carbon because a complete analysis of each size of test bar 



Shrinkage Chart 



373 



(Transactions, American Society of Mechanical Engineers, Vol. XVI, 
p. hoc) shows the same combined carbon in all sizes of many series, 
but in all cases the strength per unit of section decreased as the size 
increased. 

Strength of any size of test bar cannot be calculated by any mathe- 
matical formula from the measured strength of another size, because the 
grain changes by slow cooling. 

1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 



425 
400 
375 
350 
325 
300 
275 
250 
225 
200 
175 



3400 
3200 
3000 
2800 
2600 
2400 
2200 


- 


















^ 














^ 














^ 


M 
















y 


y" 














J 




















/ 
























^^ 


-^ 














■^ 








2x 


1" 










2000 


- 


/ 


^^' 








• 


1800 


— 




^ 




2 













1600 










. 3 


~> — — 









' 


1400 











-~^ 


^S_ 


■ 






-- 
















. 




~^ 



1.00 1.25 1.50 1.75 2.00 2,25 250 2.75 3,00 3.25 3.50, 
Percent Silicon. 

Fig. 104. 



Tensile Strength Chart. — Fig. 105 shows this chart. The dotted line 

estimated. 

" Table for Obtaining the Strength of any Size of Test Bar from the 
Measured Strength of the Standard Test Bar. — Table on p. 375 is cal- 
culated for a standard i-inch square test bar. Measure the shrinkage 
per foot of the standard test bar, then on the shrinkage chart. Fig. 105, 
find this shrinkage on the left-hand margin and follow horizontally 
until you intersect the line of the measured test bar. Follow the 
vertical line at the intersection to the top of the chart, and you find 
the percentage of silicon that is expected to produce the shrinkage. 
Find this same percentage at the top of Table i , and follow down to the 
size of test bar that you wish the strengths of. If you wish the actual 



374 



Mechanical Analysis 



strength use the lower figures as multiplier of the measured strength of 
the standard i-inch bar. If you wish the strength of a section i inch 
square by 12 inches long of the required test bar use the upper number 
to multiply by." 

"If you have the strength of any size of test bar other than a i-inch 
bar and know the silicon percentage, divide such strength by the lower 




'I. I.Z5 1.50 ir75 2.00 2Z5 ?.50 2.75 3.00 3.25 350 
Percent. 

Fig. 105. 



number for the bar, or if you have the strength of a section of the re- 
quired test bar i inch square by 12 inches long, divide by the upper 
number, and the result in either case is the strength of the standard 
I-inch bar." 

"To find the Strength of any Casting. — Divide the cubic contents of 
the casting by the square inches of cooling surface, and the quotient is 
the cooling ratio. If the casting has a large flat surface the edges may 
be neglected; for example, a casting i inch thick and 24 inches square. 



Keep's Strength Table 



375 



M I> t> 



8 8 8 -2 8 ^8 



lO O 
00 t- 
lO w 

00 t~ 



P> S 



8 8 



ft 8 



§;§ 



ro O 
00 CTi 
(^ (N 
00 00 






;^^ 



^^ eg ^ 

00 00 J> CI 



<0 (O 



00 00 l~- CO 



<0 Q fO O 

1-- o o> o 
o o <o lO 



R2 

00 to 



o> o c?> o 

to M O 



lO o 

i~0 o 
(M ro 



M l> ■'t 



t^ o 

to ^ 

CO lO 



J> ^ 



PO O to o 

00 3> 00 •* 

00 a> 00 to 



8 §S 88 



S R 



13 ^ 






:s 



376 



Mechanical Analysis 



A strip one inch wide and 24 inches long would have 24 cubic inches 
contents and 48 square inches of cooling surface. 24 ^ 48 = 0.5 ratio. 
Find this ratio at the top of the chart, Fig. 105, and follow down to the 




Iron follow-board with yokes and brass 
pasterns for test bars Yi in. square X 
12 in. long. 

Fig. 106. 



Iron Flask. 



diagonal and we find that a 2-inch square test bar represents the strength 
of the casting." 

"With the shrinkage of a standard i-inch test bar, cast at the same 
time as the casting, find on the shrinkage chart the percentage of silicon 

in the casting. Then in the Table 



Taper steel scale which measures 
shrinkage. 
Fig. 107. 




find the upper multiplier for a 2 -inch 
test bar. This multipHed by the 
measured strength of the standard 
test bar gives the strength of a sec- 
tion of the casting i inch square 
and 12 inches long." 

Mechanical analysis covers tests 
for shrinkage, strength and hard- 



Figs. 106 and 107 show a device 
designed by Mr. Keep for determin- 
ing shrinkage. 

Determinations for strength are 
generally made by taking the trans- 
verse strength and deflection. 

The Riehle Machine as shown in 
Fig. 108 is in common use for this 
purpose. 

This illustration represents faith- 
fully the general appearance of this 
machine. The specimen is shown in position. The weighing-beams 
and levers are all carefully sealed to the standard of the United States 
Government, and guaranteed to be accurate and reliable. 



Fig. 108. 



Constituents of Cast Iron 377 

Operation 

The weighing-beam must be balanced before the specimen is arranged 
for testing. The wheel shown must be moved from left to right, and, 
as the beam rises, the poise must be moved out to restore the equipoise. 
If more strain is required to break the specimen than can be weighed by 
the poise, move the poise back to zero and place the loose weight on the 
weight dish shown at the extreme left (small end) of weighing-beam, and 
move the poise out as before, until the test is completed. The calcula- 
tions are made so that the beam registers the center load. 

Dimensions 

Extreme length 3 ft. 2 in. 

Extreme height . 3 ft. i in. 

Extreme width i ft. 4 in. 

Weight 200 lbs. 

Shipping weight . 230 lbs. 

Adaptation 
Transverse specimens 12 in. long 

Hardness 

This property may be measured by embedding steel balls in the casting 
to be tested, by Turner's Scleroscope (see cut, page 114, Turner's Lec- 
tures on " Founding "); or by Keep's Machine (see cut, page 187, " Cast 
Iron "). The latter method is the more simple and gives accurate results. 
A small high speed drill may be used for this piupose, but it must be so 
arranged that the load on the spindle will be constant. 

Standard Methods for Determining the Constituents 
of Cast Iron 

As reported by the Committee of the American Foundrymen's Association, Phila- 
delphia Convention, May 21-24, IQO?- 

Determination of Silicon 

Weigh one gram of sample, add 30 c.c. nitric acid (1.13 sp. gr.); 
then 5 c.c. sulphuric acid (cone). Evaporate on hot plate imtil all 
fumes are driven off. Take up in water and boil until all ferrous sul- 
phate is dissolved. Filter on an ashless filter, with or without suction 
pump, using a cone. Wash once with hot water, once with hydrochloric 
acid, and three or four times with hot water. Ignite, weigh and evapo- 



378 Chemical Analysis 

rate with a few drops of sulphuric acid and 4 or 5 c.c. of hydrofluoric acid. 
Ignite slowly and weigh. Multiply the difference in weight by 0.4702, 
which equals the per cent of siHcon. 

Determination 0} Sulphur 

Dissolve slowly a three-gram sample of driUings in concentrated nitric 
acid in a platinum dish covered with an inverted watch glass. After 
the iron is completely dissolved, add two grams of potassium nitrate, 
evaporate to dryness and ignite over an alcohol lamp at red heat. Add 
50 c.c. of a one per cent solution of sodium carbonate, boil for a few 
minutes, filter, using a little paper pulp in the filter if desired, and wash 
with a hot one per cent sodium carbonate solution. Acidify the filtrate 
with hydrochloric acid, evaporate to dryness, take up with 50 c.c. of 
water and 2 c.c. of concentrated hydrochloric acid, filter, wash and after 
diluting the filtrate to about 100 c.c. cool and precipitate with barium 
chloride. Filter, wash well with hot water, ignite and weigh as barium 
sulphate, which contains 13.733 per cent of sulphur. 

Determination of Phosphorus 

Dissolve 2 grams sample in 50 c.c. nitric acid (sp. gr., 1.13), add 10 c.c. 
hydrochloric acid and evaporate to dryness. In case the sample contains 
a fairly high percentage of phosphorus it is better to use half the above 
quantities. Bake imtil free from acid, redissolving in 25 to 30 c.c. of 
concentrated hydrochloric acid; dilute to about 60 c.c, filter and wash. 
Evaporate to about 25 c.c, add 20 c.c. concentrated nitric acid, evapo- 
rate imtil a film begins to form, add 30 c.c. of nitric acid (sp. gr., 1.20) 
and again evaporate until a film begins to form. Dilute to about i5(» c.c 
with hot water and allow it to cool. When the solution is between 70 
degrees and 80 degrees C. add 50 c.c. of molybdate solution. Agitate 
the solution a few minutes, then filter on a tarred Gooch crucible having 
a paper disc at the bottom. Wash three times with a 3 per cent nitric 
acid solution and twice with alcohol. Dry at 100 degrees to 105 degrees 
C. to constant weight. The weight multiplied by 0.0163 equals the per 
cent of phosphorus in a i-gram sample. 

To make the molybdate solution add 100 grams molybdic acid to 
250 c.c. water, and to this add 150 c.c. ammonia, then stir until all is 
dissolved and add 65 c.c. nitric acid (1.42 sp. gr.). Make another solu- 
tion by adding 400 c.c. concentrated nitric acid to iioo c.c water, and 
when the solutions are cool, pour the first slowly into the second 
with constant stirring and add a couple of drops of ammonium 
phosphate. 



Determination of Total Carbon 379 

Determination of Manganese 

Dissolve one and one-tenth grams of drillings in 25 c.c. nitric acid 
(1.13 sp. gr.), filter into an Erlenmeyer flask and wash with 30 c.c, of the 
same acid. Then cool and add about one-half gram of bismuthate until 
a permanent pink color forms. Heat until the color has disappeared, 
with or without the precipitation of manganese dioxide, and then add 
either sulphurous acid or a solution of ferrous sulphate until the solution 
is clear. Heat until all nitrous oxide fumes have been driven off, cool 
to about fifteen degrees C; add an excess of sodium bismuthate — about 
one gram — and agitate for two or three minutes. Add 50 c.c. water 
containing 30 c.c. nitric acid to the litre, filter on an asbestos filter into 
an Erlenmeyer flask, and wash with fifty to one hundred c.c. of the nitric 
acid solution. Run in an excess of ferrous sulphate and titrate back with 
potassium permanganate solution of equal strength. Each c.c. of N-io 
ferrous sulphate used is equal to o.io per cent of manganese. 

Determination of Total Carbon 

This determination requires considerable apparatus; so in view of 
putting as many obstacles out of the way of its general adoption in cases 
of dispute, your committee has left optional several points which were 
felt to bring no chance of error into the method. 

The train shall consist of a pre-heating furnace, containing copper 
oxide (Option No. i) followed by caustic potash (1.20 sp. gr.), then 
calcium chloride, following which shall be the combustion furnace in 
which either a porcelain or platinum tube may be used (Option No. 2), 
The tube shall contain four or five inches of copper oxide between plugs 
of platinum gauze, the plug to the rear of the tube to be at about the 
point where the tube extends from the furnace. A roll of silver foil about 
two inches long shall be placed in the tube after the last plug of platinum 
gauze. The train after the combustion tube shaU be anhydrous cupric 
sulphate, anhydrous cuprous chloride, calcium chloride, and the absorp- 
tion bulb of potassium hydrate (sp. gr., 1.27) with prolong filled with 
calcium chloride. A calcium chloride tube attached to the aspirator 
bottle shall be connected to the prolong. 

In this method a single potash bulb shall be used. A second bulb is 
sometimes used for a coimterpoise being more liable to introduce error 
than correct error in weight of the bulb in use, due to change of tempera- 
ture or moisture in the atmosphere. 

The operation shall be as follows: To i gram of weU-mixed drilhngs 
add 100 c.c. of potassium copper chloride solution and 7.5 c.c. of hydro- 
chloric acid (cone). As soon as dissolved, as shown by the disappearance 



380 Chemical Analysis 

of all copper, filter on previously washed and ignited asbestos. Wash 
thoroughly the beaker in which the solution was made with 20 ex. of 
dilute hydrochloric acid [i to i], pour this on the filter and wash the carbon 
out of the beaker by means of a wash bottle containing dilute hydro- 
chloric acid [i to i] and then wash with warm water out of the 
filter. Dry the carbon at a temperature between 95 and 100 de- 
grees C. 

Before using the apparatus a blank shall be run and if the bulb does 
not gain in weight more than 0.5 milligram, put the dried filter into the 
igm'tion tube and heat the pre-heating furnace and the part of the com- 
bustion furnace containing the copper oxide. After this is heated start 
the aspiration of oxygen or air at the rate of three bubbles per second, to 
show in the potash bulb. Continue slowly heating the combustion tube 
by turning on two burners at a time, and continue the combustion for 
30 minutes if air is used; 20 minutes if oxygen is used. (The Shimer 
crucible is to be heated with a blast lamp for the same length of 
time.) 

When the ignition is finished turn o2 the gas supply gradually so as 
to allow the combustion tube to cool off slowly and then shut off the 
oxygen supply and aspirate with air for 10 minutes. Detach the potash 
bulb and prolong, close the ends with rubber caps and allow it to stand 
for 5 minutes, then weigh. The increase in weight multiplied by 0.27273 
equals the percentage of carbon. 

The potassium copper chloride shall be made by dissolving one pound 
of the salt in one litre of water and filtering through an asbestos 
filter. 

Option No. I. — While a pre-heater is greatly to be desired, as only 
a small percentage of laboratories at present use them, it was decided 
not to make the use of one essential to this method; subtraction of the 
weight of the blank to a great extent eliminating any error which might 
arise from not using a pre-heater. 

Option No. 2. — The Shimer and similar crucibles are largely used as 
combustion furnaces and for this reason it was decided to make optional 
the use of either the tube furnace or one of the standard crucibles. In 
case the crucible is used it shall be followed by a copper tube He inch 
inside diameter and ten inches long, with its ends cooled by water jackets. 
In the center of the tube shall be placed a disk of platinum gauze, and 
for three or four inches in the side towards the crucible shall be silver foil 
and for the same distance on the other side shall be copper oxide. The 
ends shall be plugged with glass wool, and the tube heated with a fish 
tail burner before the aspiration of the air is started. 



Graphite 381 

Graphite 
Dissolve one-gram sample in 35 c.c. nitric acid [1.13 sp. gr.], filter on 
asbestos, wash with hot water, then with potassium hydrate [i.i sp. gr.] 
and finally with hot water. The graphite is then ignited as specified in 
the determination of total carbon. 



CHAPTER XVI 
MALLEABLE CAST IRON 

The process of rendering iron castings malleable was discovered by- 
Reaumur in 1722 and is essentially the same as that pursued at the 
present day. 

McWilliams and Longmuir divide malleable castings into two classes. 

1. Black Heart 

Black heart has a silvery outside and black inside, with a silky 
lustre. This is made of a hard white iron, containing from 3 to 4 per 
cent carbon, as hard carbide of iron. 

By the process of annealing, to be described later, the carbide of iron 
is decomposed into free carbon (annealing carbon) and iron; leaving a 
soft malleable iron, which contains nearly all of the initial carbon but 
in the free state finely divided and intermixed with the iron. 

Black heart is mostly made in America. The process is conducted 
much more rapidly than that of the ordinary (or Reaumur process), but 
requires more skill and scientific information. The iron used must be 
low in silicon and sulphur but need not necessarily be a white iron. 

The analysis should approximate to, silicon, i per cent to 0.5 per cent; 
sulphur, .05 per cent as a maximum; phosphorus, .1 per cent maximum; 
manganese, .5 per cent maximum and carbon 3 per cent. 

The principle involved is that of taking white iron castings of suitable 
composition, heating them to high temperature and converting them to 
the malleable condition by precipitating the carbon in a fine state of 
division, as annealing carbon. High temperature shortens the process, 
but it has been found more desirable to use a lower temperature and 
longer anneal, as the desired change is more readily secured. 

The method of molding is the same as for gray iron, with same allow- 
ance for shrinkage. The amount of feeder required varies from 12.5 
to 25 per cent of the weight of casting. Skill is required to make solid 
castings with minimum amount of metal. 

After cleaning in the usual manner the castings are packed in cast iron 
boxes of varying sizes to suit their character, with iron scale or sand, 
bone dust or fire clay; the boxes are covered with lids and luted, then 

382 



Black Heart 



383 



stacked in the annealing oven (to be described later). The temperature 
of the oven is gradually raised to about 1 100° C, maintained at that point 
for two days and then allowed to drop slowly until sufficiently cool to 
permit removal of the boxes. 

The composition of the castings after annealing is only altered in the 
carbon, the total amount being somewhat less but practically all present 
in the free state. The composition of castings made by one of the 
largest English makers is as follows: 

Si 0.5; S 0.04; P. 0.07; Mn 0.4; graphitic carbon 2.5; combined 
carbon 0.05. A test piece i/^-inch square bent 180° — cold; tensile 
strength 40,000 pounds per square inch, elongation 6 per cent in 2 inches, 
reduction of area 9 per cent. 

Black heart is more reliable for light than for heavy work. To avoid 
the introduction of sulphur, the pig iron is usually melted in an air 
furnace. 

Messrs. Charpy & Grenet's experiments on irons of the following 
compositions are given herewith. 



No. 


Silicon 


Sulphur 


Phosphorus 


Manganese 


Carbon 


I 


.70 


.01 


trace 


.03 


3.60 


2 


.27 


.02 


.02 


trace 


3.40 


3 •• 


.80 


.02 


.03 


trace 


3.2s 


4 


1.25 


.01 


.01 


.12 


3.20 


^ 


2.10 


.02 


.01 


.12 


3.30 



These irons were poured into cold water and contained no appreciable 
amount of graphite, excepting the last which had 20 per cent. Samples 
of these were subjected to various reheatings and to ascertain as nearly 
as practicable the condition at any one temperature, the samples were 
quenched at that temperature and then analyzed. 

1. Heated at 1100° C. or any low temperature for long periods gave 
no graphitic carbon; but at 1150° C. the separation of graphitic carbon 
was produced. 

2. Heated for four hours each at 700°, 800°, 900° and 1000° C. showed 
no free carbon; but it appeared in heating to 1100° C. 

3. Showed traces at 800° C. 

4. 5. Showed traces at 650° C. 

In the case of No, 5, after heating at 650° C. for 6 hours, the content 
of graphitic carbon had increased from o.io to 2.83 per cent. 

The separation of graphite, once commenced, continues at tempera- 
tures inferior to those at which the action begins. 

Thus: A sample of No. i, heated at 1170° C. and quenched, contained 



384 



Malleable Cast Iron 



only 0.50 graphitic carbon and 2.6 combined carbon, while another 
sample of the same cast iron, heated at the same time to 1170° C, cooled 
slowly to 700° C. and then quenched contained 1.87 graphitic carbon 
and 0.43 combined carbon. 

Again a fragment of No. 3, heated to 1170° C. and quenched, contained 
1.42 graphitic carbon and 1.69 combined carbon, while another fragment 
heated to 1170° C. cooled slowly to 700° C. and then quenched contained 
2.56 graphitic carbon and 0.38 combined carbon. 

At a constant temperature the separation of the graphite is effected 
progressively, at a rate that is the more gradual, the lower the tempera- 
ture or the less the silicon content. 

The authors show that these cast irons, with regard to the critical 
points, have the usual carbon change point, about 700° C, but that there 
is another well-marked arrest in heating at 1140°, 1165°, 1137° and 
1165° C, for numbers i, 2, 3, 4 and 5, respectively; and similarly in 
cooling at 1120°, 1130°, 1137° and 1145° C. 

In an experiment made by W. H. Hatfield, with six bars, all containing: 

Si i.o; S 0.04; P 0.04; Mn 0.22; graphitic carbon 2.83; combined 
carbon 0.08, all white irons as cast; variously heat-treated so as to give 
the same composition to analysis, but to have the free carbon in all 
states of division from fine in No. i to coarse in No. 6. 

Bars I inch square by 18 inches long were tested transversely on knife 
edges 12 inches apart and gave 



No. 


Inches 
deflection 


No. 


Inches 
deflection 


I 




5 

6 




2 


3 



before fracture; the gradually decreasing deflections given being due 
entirely to the increasing coarseness of the free carbon. 

Another set of four test bars, containing 0.45, 0.90, i.ia-i.88 per cent 
sihcon but otherwise similar in composition to the above; heat-treated 
so that all should have the same type of free or annealing carbon, gave 
95°, 98°, 94° and 89°, respectively, when subjected to the ordinary 
bending test. 

The microstructure of these bars consisted of ferrite or silicon ferrite 
speckled with annealing carbon, which if kept of suitable structure affects 
the malleability little more than does the slag in the case of wrought 



Ordinary or Reaumur Malleable Cast Iron 



385 



Pearlite, when present, after heat-treating white irons, greatly in- 
creases the tenacity, one sample having a tenacity of 32,6 tons per square 
inch, with an elongation of 6 per cent on 2 inches, and a bending angle 
of 90°, when treated so as to leave 0.35 per cent of carbon in the com- 
bined form and present as pearlite in the structure. 

Another sample of the same general composition, but treated to leave 
only 0.06 per cent as combined carbon had a tenacity of 21.2 tons per 
square inch, elongation 11 per cent on two inches and a bending angle 
of 180° unbroken. 



2. Ordinary or Reaumur Malleable Cast Iron 

In this class of castings the carbon is completely eliminated, leaving 
a soft material similar in analysis to wrought iron. 

It is stated that irons containing as much as 0.5 sulphur may be used 
in this class of castings. The irons employed are mottled or white, 
analyzing as follows: Si 0.5 to 0.9; S 0.25 to 0.35; P 0.05 to 0.08; Mn 
0.1 to 0.2, total carbon 3^ per cent 

It may be melted in the crucible, in the cupola, or in the air fiu-nace. 
The cupola is more in general use in England than the air furnace. 

The table below shows approximately the influence of remelting by 
the several processes. 



Original pig 
iron 


Crucible 


Cupola 


Reverb. 


Siemens 


C 3.S 

Si 8s 

S 25 

Mn 20 

P 05 


3.4 
.82 
.30 
.10 
• OS 


3.4 
.75 
.31 
.10 
.054 


3.2 
.65 
.27 
.10 
.052 


3.2 
.70 
.26 
.10 
.05 



Whichever furnace is used it is necessary to have the metal fluid 
enough to fill the most intricate parts of the molds to be poured in any 
one batch. Molding operations are the same as for green sand, except 
that provision must be made for the narrow range of fluidity and the 
high contraction of white iron. 

Allowance for shrinkage is }i inch to the foot. The castings after 
proper cleaning are packed in cast-iron boxes of suitable sizes, with red 
hematite ore broken up finely. New ore is not used alone but one 
part new is mixed thoroughly with four parts that have been used 
before; the castings are carefully packed in this mixture so that no 
two are in contact. 

The oxygen from the ore oxidizes the carbon in the castings, gradually 



386 



Malleable Cast Iron 



eliminating it. The ore, previous to use, is red oxide of iron (Fe203), 
but after the annealing process is found to be black oxide corresponding 
to the formula Fe304. 

After stacking the boxes in the anneaHng oven, the temperature is 
gradually raised during 48 to 72 hours; maintained at the annealing 
temperature from 12 to 24 hours, then allowed from 48 to 72 hours to 
cool. 

The length of time during which the high temperature is maintained 
varies with the thickness of the castings. For thick work the high 
temperature may have to be continued for a period increasing with the 
thickness of the, castings up to 96 hours. 

Typical Temperature Curve for Annealing Oven 

1000 



500 



O'C 






1 2 



3 4 5 6 
Fig. 109. 



Some makers anneal at as low a temperature as 850° C. (see P. Long, 
"Metallurgy, Iron and Steel," page 130). Within reasonable hmits, 
chemical composition of the castings in this process has little bearing 
on the result provided they are white iron as cast. 

The silicon may run from 0.3 to 0.9; sulphur 0.05 to 0.5; phosphorus 
should be under o.i; manganese causes trouble if over 0.5. 

Castings made by this process give a tensile strength of 18 to 22 tons; 
an elongation of 2V-i. to 6 per cent on 2 inches and a reduction of area of 
5 to 8 per cent, with a cold bend on i^-inch square, of 45° to 90°. 

Mr. P. Longmuir obtained the following results from a commercial 
casting: Tensile strength, 27 tons; elongation, 5.7 per cent on 2 inches; 
reduction of area 10 per cent; it analyzed Si 0.65; S 0.3; P 0.04; 
Mn 0.15. 

In the process of annealing the carbon only is affected, being con- 
siderably reduced in amount; what remains is partly free and partly 
. combined. An annealed sample containing 0.6 per cent free carbon and 
0.4 combined is considered good. 

Mr. Percy Longmuir places the average silicon for good malleable 
castings at 0.6, sulphur 0.3, phosphorus 0.05, and combined carbon 3 
to 3.5 per cent. 



Ordinary or Reaamiir Malleable Cast Iron 387 

Analyses Before and After A.nnealing 



Constituents 


Iron as 

cast 


After pro- 
longed an- 
nealing in 
iron ore 


Total carbon 


3.43 
.45 
.06 
.31 
.53 


10 


Silicon 


45 


Sulphur 


06 


Phosphorus 


32 


Manganese 


53 







Interesting experiments were made by Mr. W. H. Hatfield of Sheffield, 
and results published in ''The Foundry," Oct., 1909, by Mr. G. B. 
Waterhouse. 

"Three converted bars of identical composition analyzing: 



Constituents 


Per cent 


Constituents 


Per cent 


Total carbon 

Combined carbon 


1.64 

1.64 

.03 


Manganese 

Sulphur 

Phosphorus 


trace 
01 


Silicon 


.01 



One was packed in charcoal, another in pure quartz sand, the third 
in a red hematite ore mixture, consisting of two parts old and one part 
new. The pots were placed close together in the annealing oven and 
slowly raised to about 800° C. This required about three days. They 
were held at this temperature for 24 hoxirs, then raised to 900° C, held 
there for two days, then cooled slowly. Upon removal and breaking 
the following results appeared. 

No. I, from charcoal, broke short and gave a coarsely crystalline 
structure showing imder the microscope absolutely no free carbon. 

Its carbon was 1.63 per cent, the other elements remaining unchanged. 

No. 2, from sand, Was fairly tough but broke without bending. 
Fracture crystalline and steely. Its carbon was 0.74 per cent and again 
no free carbon was found. 

No. 3, from the ore mixture, bent considerably before breaking 
and was fairly ductile. Its carbon was 0.15 per cent and again no 
free carbon could be found, the structure being of ferrite crystals. 
The experiments appearing to prove conclusively the possibihty of 
carbon being removed without previous formation of free or temper 
carbon. 



388 



Malleable Cast Iron 



For the second series of experiments, an ordinary white iron was 
taken containing: 



Constituents 


Per cent 


Constituents 


Per cent 




3.5 

none 
.50 


Manganese 

Sulphur 

Phosphorus 


Trace 




.35 











The packing was the ore mixture previously referred to. 

Samples were heat-treated and sections were given a careful micro- 
scopical examination, with the following results: 

Decarburization began 54 hours after commencement of heating and 
at 770° C, showing a thin skin of ferrite; the remaining portion of the 
casting retained the typical structine of white iron. 40 hours later, 
during which time the temperature gradually raised to 980° C, the de- 
carburized skin increased in thickness to Yis inch. 

Fourteen hoiurs later, at a temperature of 970° C, the interior had 
broken down and free or temper carbon was apparent. During the 
next interval' of 60 hours, at 950° C. very little change occurred. The 
center showed pearlite, with a little cementite and containing temper 
carbon, merging gradually into the skin of ferrite. 

During the following 72 hours, the temperature was dropped to 
140° C, resulting in the production of a really good sample of Enghsh 
malleable cast iron of the following analysis: 



Constituents 


Per cent 


Constituents 


Per cent 


Combined carbon 


.65 
1. 10 


Sulphur 


■ 35 


Temper carbon 


Phosphorus . ... 


■ 05 




1 





The author's conclusion is, that carbon is eHminated while still in 
combination with the iron. 

It (the elimination) begins to take place at the comparatively low 
temperature of 750° C, and increases in activity with the temperature 
imtil such a temperature is reached that free or temper carbon is pre- 
cipitated. 

Previous to this change the interior consists of white iron, with the 
original quantity of combined carbon. 

As the operation proceeds the temper carbon is gradually taken back 
into combination to replace that removed by the oxidizing influences. 



American Practice 389 

American Practice 

The mixtures of iron vary as the castings are thick or thin. The iron 
is melted either in the cupola, the air furnace or the open hearth furnace. 
The latter produces the best castings, but can only be used advanta- 
geously where the output is large enough to permit of running the fur- 
nace continuously. 

The air furnace is most frequently used. 

The castings may or may not be packed in an oxidizing material. 
Sand or fire clay are frequently used. 

Dr. Moldenke, who is recognized as an authority on malleable cast 
iron, states: "That it is absolutely necessary to have the hard castings 
free from graphite." He advises the following: 

Contents: Per Cent 

Carbon 3 -3.5 

Silicon, heavy work, not over 0.45 

Sihcon, ordinary work, not over o . 65 

SiHcon, agricultural work, not over o. 80-1 . 25 

Sulphur, not over o . 05 

Phosphorus, not over o. 225 

Manganese, not over o. 40 

"In anneaKng, the temperature of the furnace should be run up to 
' heat' in the shortest safe time possible; the limit is the danger of injury 
to furnace. Then the dampers should be closed and the temperature 
evenly maintained for 48 hoiurs. The fiu"nace should then be gradually 
cooled to a black heat before dumping. 36 hovirs are usually required 
to bring the oven up to heat. 

The entire process occupies about seven days. The annealing tem- 
perature is 1350° F. and this must obtain at the coldest part of the fur- 
nace, usually the lower part of the middle of the front row of pots. 

A difference of 200° F. in temperature is often found at different 
parts of the furnace. 

Cupola iron requires an annealing temperature 200" F. higher than 
that frorri an air furnace. 

The fuel ratio of an air furnace runs from i to 2 to i to 4. 

Loss in sihcon about 35 points. 

Temperatures should be carefuUy watched and measured with a 
Le Chateher pyrometer." 

The Doctor has much to say about the danger of injury to the melted 
iron in the bath, from oxidation. His practice was to have three tapping 
spouts at different levels, so that for an 18-ton furnace, three taps of 
6 tons each may be made at intervals, tapping at the upper hole first 
and then in order from upper to bottom hole. 



390 Malleable Cast Iron 

Mr. H. E. Diller, in the Journal of The American Foundrymen's 
Association, Vol. XI, Dec, 1902, says: 

The hard casting should have its carbon practically all in the com- 
bined state, while the annealing process should convert this to the so- 
called temper, or annealing carbon. 

In the manufacture of malleable castings the special make of iron 
called 'Malleable Bessemer' or 'Malleable Coke Iron' is the principal 
material used. The charcoal irons, while unequalled for value, are con- 
fined to the regions where they can compete with the cheaper coke 
irons. 

The composition required is as follows: 

Per cent 

Silicon o . 75 to 1 . 50 

Sulphur, below 0.04, if possible 

Phosphorus, under ....0.20 

With the pig iron, hard sprues (unannealed scrap), steel and also malle- 
able scrap are charged. The latter two materials are very good to add 
to the mixture, as they raise the strength of the casting very consider- 
ably. • 

Too much must not be added, as it would reduce the carbon to a 
point where fluidity and life in the melted metal is sacrificed. 

The most serious objection to cupola iron is its poor behavior under 
bending test, the deflection being very slight. Test bars from this 
class of iron seldom run above 40,000 pounds per square inch in tensile 
strength, while with furnace iron, there is no difficulty in getting a few 
thousand pounds more. 

The metal may be tapped from the furnaces into hand ladles; or it 
may be caught in crane ladles, carried to the distributing point and there 
emptied into the hand ladles. 

When tapped into hand ladles, time is a serious item, for the begin- 
ning and the end of the heat will be two different things. The latter 
iron will be inferior as it was subjected to the oxidizing effect of 
the flame much longer than the first part. This difficulty is some- 
what remedied by pouring the light work first, the heavier pieces 
coming later, when the silicon has been lowered too much for good light 
castings. 

The gating should be done to avoid the shrinkage effects as much 
as may be. The little tricks that can be applied make a surprising 
difference in the molding loss. Some malleable works seldom lose 
more than 10 per cent, while in others 20 per cent and over is the 
rule. 

'After the castings have been tumbled they go to the annealing room, 



American Practice 



391 



where they are packed in mill cinder or iron ore, in cast-iron boxes. 
These are carefully luted up and heated in suitably constructed ovens, 
for five or six days. 

It usually takes from 36 hours to 48 hours to get the oven up to heat, 
the temperature ranging from 1600° to 1800° F. in the oven, the boxes 
having a somewhat lower temperature at the coldest point. 

When the fires are extinguished, the dampers are closed tight, all 
air excluded, and the oven allowed to cool very gradually; often only 
400"^ F. the first day. 

After the castings come from the anneahng oven, they are again 
tumbled to remove the burnt scale; then chipped and ground for ship- 
ment. 

A well-annealed casting should not have much over 0.06 to 0.12 
per cent combined carbon remaining in it. There is a material difference 
between the strength of an over-annealed casting and a normal one. 




Fig. 1 10. — Typical American Air Furnace. 

Two bars were taken from each of five heats. One from each set 
was given the usual anneal and the others reannealed. The average 
tensile strength of those annealed as usual, was 50,520 pounds per 
square inch, and the average elongation 6% per cent in six inches. 

The reannealed set had an average tensile strength of 43,510 pounds 
per square inch; the average elongation was 6h per cent in six inches. 
Over anneahng had therefore cost the metal some 7000 pounds of its 
strength. 

'Malleable' can be made up to 60,000 pounds per square inch, though 
this is not advisable as the shock resisting qualities are sacrificed. 

Prof. Ledebur determined by experiment that the higher the silicon 
the lower the annealing temperature required, and the higher the tem- 
perature and silicon the quicker the change. He used five samples: 

1 with 0.07 silicon. Could not be annealed. 

2 with 0.27 silicon. Required temperature almost at melting point. 

3 with 0.80 siHcon. Began to anneal at 1675° F. 

4 with 1.25 sihcon. Began to anneal at 1200° F. 

5 with 2.10 silicon. Began to anneal at 1200° F. 



392 



Malleable Cast Iron 



Specifications for Malleable Castings of J. I. Case Co. 

Tensile strength per sq. in., 35,000 to 50,000. 

Elongation, 1.5 in 4 in. 

Transverse test for O bar .8 inch diameter on supports 12 inches 
apart, must show 1750 pounds to 2,400 pounds breaking strength and 
deflection of not less than 0.31 inch. 

Drop Test. — A bar .8 inch diameter on supports 12 inches apart must 
not break under less than 1650 inch pounds, the drop being 22 poimds 
and the first drop through 3 inches, second 4 inches and so on imtil 
rupture occurs. 

Tortional test should closely approximate the tensile strength. 

Bending Test. — Pieces from Me to %& inch thick and from i to 
3 inches wide, should bend over on themselves, around a circle equal 




Fig. III. — Annealing-Oven equipped for Gas. 

in diameter to twice the thickness of the piece and bend back again 
without break. 

The anneal is specified at not less than 72 hours for light and 120 hours 
for heavy work. 



Comparison of Tests made in 1885 ivith those made in igo8 
1885 By Prof. Ricketts 

%-inch D bar, tensile strength, 30,970 to 44,290 per square inch. 
Elongation, 1.8 inches in 5 inches. 

Bars I by .2,2,, tensile strength, 32,750 to 36,990 per square inch. 
Round bars, i/i inch diameter, tensile strength, 36,200 to 44,680 per 

square inch. 
Round bars, % inch diameter, tensile strength, 26,430 to 34,600 per 

square inch. 
Compression, 108,900 to 160,950 pounds per square inch. 



American Practice 393 

igo8 

Bars H-inch D, tensile strength, 52,000 to 59,000 per square inch. 
Larger sections, tensile strength, 42,000 to 47,000 per square inch. 
Dr. Moldenke states that the tensile strength should run from 40,000 

to 44,000. 
The Iron Trade Review gives the production of malleable castings in 

1903 for the United States and Canada as 750,000 tons. 
Combined output of the rest of the world 50,000 tons. 



CHAPTER XVII 



STEEL CASTINGS IN THE FOUNDRY 



There is a great demand on the part of foundrymen for an appliance 
to successfully melt steel in smaU quantities; permitting small steel 
castings, or castings for which the demand is immediate, to be made in 
the gray iron foundry. Many efforts have been made to realize this 
desire, but so far have met with indifferent success. There are several 
appHances offered to manufactiirers, some employing the Bessemer 
converter, others the electric furnace in connection with the cupola. 

Men especially skilled are required to manipulate steel furnaces. The 
processes of mixing and melting the metal and annealing castings differ' 
so radically from those of the gray iron foimdry, that in the present 
undeveloped state of steel founding on a small scale, steps on the part 
of the foundryman in that direction should be taken with extreme 
caution. 

Mr. Percy Longmuir defines ordinary steel "as iron containing from 
O.I to 2 per cent of carbon in the combined form, which has been sub- 
mitted to complete fusion and poured into an ingot, or mould, for the 
production of a malleable or forgeable metal." 

"Mild steel contains about 0.2 per cent carbon; the element increasing 
as the harder varieties are approached, being highest of all in the tool 
steels." 

"The mechanical effect of this carbon is shown in the following table." 



Material 


Carbon 


Silicon 


Sulphur 


Phos- 
phorus 


Tenacity 

in tons 

per square 

inch 


Extension 
per cent 
on two 
inches 


Contrac- 
tion 
per cent 
of area 


Mild steel.... 
Tool steel 


.10 
1. 00 


.03 
.03 


.02 
.02 


.02 
.02 


20.00 
60.00 


50.0 
5.0 


70.0 
10. 



"Within limits, an increase of carbon is accompanied by an increase in 
tenacity and a decrease in ductility, each increment of carbon showing 
distinctly these increases." 

"The following classification embraces the most famiUar tempers of 
Bessemer, Siemens and crucible steel." 

394 



Steel Castings in the Foundry 



395 



Class of steel 




Content 

of carbon 

.20 


Purpose 






Ship and boiler plates, sheets, etc. 




.25 


Axle steel. 


Bessemer steel 


■•i 


.03 


Tire steel. 






.03 


Rail steel. 




..1 


.50 


Spring steel. 




.20 


Boiler plate. 


Siemens or open hearth . . 


.65 


Spring steel. 




I 


1.30 


Tool steel. 




r 


.90 


Chisel steel. 




! 


1. 10 


Large files, drills and similar tool steels. 


Crucible steel 


.J 


1.20 
1.40 


Turning tool steels. 




Saw file steels. 






1.50 


Razor steels. 



A steel containing o.io per cent carbon is unaffected in hardness by 
quenching, while one containing i per cent carbon becomes so hard under 
same conditions that it will scratch glass. 

Manganese is present in all commercial steels, varying from traces up 
to I per cent. It promotes soundness and neutralizes the effect of 
sulphur. 

Sihcon tends to the production of sound metal; while it is present in 
insignificant quantity in forging steel, in casting steels it may exist to the 
extent of 0.3 per cent. 

Phosphorus produces an exceedingly brittle, cold short metal. Pure 
steels contain 0.02 to 0.03 per cent. 

Usual specifications limit the phosphorus content to 0.06; at o.i the 
danger limit is reached. 

Steels containing appreciable amounts of sulphur are red short. In 
high quahty of steels the sulphur content runs about o.oi per cent. 
Ordinary specifications place the limit at 0.04 per cent. 

The variations in the carbon content to suit various requirements are 
shown in the following table : 



Content of 

carbon in 

steel 


Purpose for which the steel, in the form of a hardened or 


tempered tool, is suitable 


.50 


Springs. 


.60 


Stamping dies. 


.65 


Clock springs. • 


.75 


Hammers, shear blades, axes, mint dies. 


.80 


Boiler punches, screw dies, cold sets. 


.90 


Edge tools, slate saws. 


.95 


Circular saws, pins. 


I. CO 


Cold chisels, cross-cut saws. 


1. 10 


Drills, large files, hand saws, mill picks. 


1.20 


Granite and marble saws, mill chisels. 


1.30 


Harder files, cutters, spindles, turning tools. 


1.40 


Saw files. 


1.50 


Turning tools for chilled rolls, razors and surgical instruments. 



396 



Steel Castings in the Foundry 



The following table is taken from Prof. J. O. Arnold's "Influence 
of Carbon on Iron." 

Mechanical Properties "Normal Steels" 



Carbon 


Elastic limit, 

tons per 
square inch 


Maximum 
stress, tons 
per square 
inch 


Elongation 


Reduction 
of area 


.08 
.21 
.38 
.59 
■89 
1.20 
1-47 


12.19 
17.08 
17.95 
19.82 
24.80 
35.72 
32.27 


21.39 
25.39 
29.94 
42.82 
52.40 
61.64 
55.71 


46.6 
42.1 
34.5 
19.9 
I3-0 
8.0 
2.8 


74 
67 
56 
22 
15 
7 
3 


8 
8 
3 
7 
4 
8 
3 



"Normal steels" represent the rolled bars heated to 1000° C. and 
cooled in air. 

" Comparing this table with the foregoing statements, it appears that 
as pearlite replaces ferrite, the maximum stress increases, continmng 
to do so until a structure consisting of pearlite and very thin meshes of 
cementite is reached. Further increase in carbon resulting in greater 
dispersal of free cementite is associated with a decrease in maximum 
stress"." 



Bessemer Process 

The Bessemer process consists in blowing a large volume of compressed 
air through a bath of molten pig iron; the oxygen of the air combining 
with carbon, sihcon and manganese to form oxides. That combined 
with carbon passes off as gas while with sihcon and manganese slags are 
formed. 

On removal of carbon, silicon and manganese, assmning that sulphur 
and phosphorus are low, a product resembling wrought iron is obtained. 
Meantime during the process of oxidation, there is a rise in temperature 
sufficient to maintain mild steel in a fluid condition. The oxidation of 
silicon has the greatest effect in producing the rise in temperature. The 
irons must be low in sulphur and phosphorus, as these elements are not 
removed. An average content of 2.5 per cent silicon in the pig iron gives 
the best results. Higher than this, the heats are Hable to require scrap- 
ping; while with a lower content of sihcon there is danger of "cold 
blows." The melted metal is taken directly from the cupola, led by 
runners to the converter. 



The Baby Converter 



397 



The Baby Converter (Robert) 

This consists of a steel shell mounted on trunnions, so that it may be 
properly rotated. It is flattened on the back and lined with silica brick 
or ganister. On the flattened side the tuyeres are introduced horizontally. 

The surface of the metal lies approximately at the bottom of the 
tuyeres so that the blast may impinge upon it. The blast is from 3 to 
4 pounds per square inch and means are provided for regulating it. The 
tuyeres being inclined radially, a rotary motion is imparted to the molten 
metal by the blast. 

In some cases the surface of the metal may be above the tuyere level, 
but seldom exceeds that by more than three or four inches. The high 
tuyere level permits some of the air to escape and burn on the surface 
of the bath; carbon monoxide is formed in the bath by the oxidation of 
the carbon. 

The combustion of carbon monoxide gives rise to considerable heat, 
which is absorbed by the bath. To this reaction is due the higher tem- 
perature of the side blow converter. 

The Tropenas converter has a double row of tuyeres which are hori- 
zontal when the converter is vertical. They are not radially inclined 
as in the Robert. The surface of the metal is at the bottom edge of the 
lower row of tuyeres; the blast is always on the surface of the metal. 

When blowing the converter is slightly inchned, causing the direction 
of the tuyeres to slope towards the surface of the metal. During the 
early stage of the blow the lower tuyeres only are used; but on the 
appearance of the carbon flame the upper row is opened. The carbon 
monoxide, partly consumed by air from the lower tuyeres, is supplied 
with sufi&cient oxygen for complete combustion by that from the upper 
row, generating additional heat. 

Recarbonization is effected in the converter or in the ladles according 
to the character of the composition required. 

The chemical changes taking place in a two ton Tropenas converter 
are given as follows : 



Constituents 


Cupola 
metal 


After 5 
minutes 
blowing 


After 12 
minutes 
blowing 


After 14 
minutes 
blowing 


After 18 
minutes 
blowing 


End of 
blow 


Fin- 
ished 
metal 


Graphite 

Combined car- 
bon 

Silicon 

Sulphur 

Phosphorus 

Manganese 


3.180 

.350 
2.310 
.037 
.054 
.610 


2.920 

.340 
1.620 
.037 
.053 
.600 


2.900 
.466 
.035 
.054 
.101 


2.300 
.382 
.036 
.054 
.040 


.860 
.084 
.038 
.051 
.040 


.100 

.074 
.038 
.050 
.042 


.240 
.326 
.037 
.0S8 
1.080 



398 Steel Castings in the Foundry 

Theoretically the feeder on a steel casting should sink due to shrinkage. 
If, however, instead of sinking, a rise is shown, this is clear evidence of 
internal unsoundness or sponginess. To prevent this result one of the 
first essentials lies in having the steel thoroughly dead melted or "killed" 
before casting. A properly "killed" steel pours quietly and settles 
down gently in the mould. "Wild metal " acts in the opposite way and 
in some cases is represented by an over-oxidized metal. 

A distinction must be drawn between a "pipe" and a blow hole. 

The former is due entirely to contraction or shrinkage in passing from 
the Hqmd to the solid state and must be obviated by feeding. 

"Blow-holes" are entirely different from "pipes" and are formed by 
the hberation of gases absorbed during the melting process. 

In considering the character of these gases, oxygen naturally arises 
first, owing to the strong affinity between iron and oxygen. There is 
every reason to suppose, however, that the oxygen absorbed when the 
iron is molten, remains stable at low temperatures -as an oxide, and in 
the absence of a deoxidizing agent this ferrous oxide is intermingled with 
the iron. Oxygenated steel is "dry" under the hammer and this con- 
dition is not necessarily due to blow-holes, but to "red-short" metal. 
Further, if free oxygen were present in quantity in the gas contained in 
a blow-hole, its skin would show an oxide film. 

The majority of blow^-holes have bright surfaces; comparatively few 
show colored tints, ranging from a straw to a blue, due to oxidation. 
These colored blow-holes owe their oxidized film, not to free oxygen 
hberated by the iron, but to air mechanically trapped during casting. 
Analyses of the gases seldom show more than traces of oxygen. Mr. E. 
Munker reports sixty-seven analyses of gases evolved by molten pig 
iron; the highest content of oxygen in the series is found at 0.8 per cent. 
Average analyses of gases in blow-holes give results of the following 
order: Per cent 

Hydrogen 75 

Nitrogen . 23 

Carbon monoxide . 2 

The actual amount of these gases absorbed depends to some extoit 
on the temperature and composition of .the bath. While fluid the gases 
are retained; but with a fall in temperature after casting they are evolved. 
Those set free by a fall in temperature bubble through the pasty mass, the 
trapped bubbles representing blow-holes in the casting. As the tem- 
perature continues to fall less movement is offered and the gases cannot 
force passages through the stiffening metal. Hence more bubbles are 
trapped. Finally a stage is reached at which the mass becomes rigid 
and the further formation of blow-holes becomes impossible. 



The Baby Converter 



399 



The author's conclusions from the investigations of Wahlberg are: 

"i. If no internal movement is possible in the solidifying steel, the 
gas cannot disengage itself and so leads to the formation of blow-holes." 

"2. The presence of sihcon and manganese lead to the retention of 
the gases until sohdification is complete, hence preventing the formation 
of blow-holes." 

Methods of prevention include: 

"i. Liquid compression. 

"2. Additions to the steel of sihcon, manganese or aluminum. Each 
of these elements acts powerfully on the oxygen or the oxides of iron, 
combining with the oxygen to form slag." 

" Aluminum will remove carbonic oxide. There is, however, no reason 
to suppose that it will remove either hydrogen or nitrogen." 

"There are grounds for the belief that silicon, manganese and alum- 
inum increase the solvent power of the steel for hydrogen and nitrogen 
and that these gases remain dissolved." 

BrineU found that to produce an ingot of perfect density in the absence 
of sihcon, 1.66 per cent of manganese is necessary. In the absence of 
manganese 0.32 per cent sihcon is required; and with no manganese or 
sihcon 0.0184 per cent of aluminum is sufficient to produce a perfectly 
sound ingot. Or expressed in another way he states that aluminum is 
90 times as effective as manganese and 17.3 times as much so as sihcon, 
in removal of gases. 

Metalhc borides are suggested by Weber for removal of oxygen; these 
in conjunction with ferrotitanium tend to removal of nitrogen. 

The casting temperature exercises a great influence upon the properties 
of the metal. These are found to rise and fall with the temperature 
above and below the casting heat, as shown by the following table: 



Analyses 


Maximum 

stress, 

tons per 

square 

inch 


Elonga- 
tion, 
per cent 

in 
2 inches 


Reduc- 
tion of 


No. 


Carbon 


Si 


Mn 


s 


P 


per cent 


80 A.... 

81 A.... 

82 A.... 

83 A.... 


.29 
.29 
.29 
.29 


.07 
.07 
.07 
.07 


.16 
.16 
.16 
.16 


.07 
.07 
.07 
.07 


.c6 
.06 
.06 
.06 


24.2 
27.2 
27.0 
25.5 


95 

24.0 
12.5 
8.0 


18.0 
32.3 
17-5 
12.0 



These steels were poured from one large ladle at intervals of a few 
minutes. They are exactly of the same analysis; the bars were annealed 
together, each bar receiving exactly the same treatment, and apart from 
variation of casting temperatures, the conditions were the same for all. 
These results have been repeated many times. When the steel is poured 
at an excessive temperature, similar ones are always obtained. 



400 



Steel Castings in the Foundry 



Annealing 

The following is extracted from McWiUiams and Longmuir's " Gen- 
eral Foundry Practice." 

Steel castings are usually annealed in the reverberatory gas furnace. 
The anneaKng recommended by Prof. Arnold for general work is to heat 
the castings up to about 950° C. keeping them at that temperature for 
about 70 hours, then luting the furnace and allowing them to cool slowly 
for 100 hours. 

The Clinch- Jones annealing furnace is highly spoken of, the controlling 
idea being that while the castings are heated in a muffle, by keen flames 
outside the walls of the muffle, virgin gas from the producer is allowed 
to come into the muffle and combine with all the oxygen that may enter, 
thus preventing it from getting to the castings to scale them by oxidizing 
at their surfaces. A cut of this oven is shown on page 266 (McW. &L.). 

The micrographs (McW. & L.) show the structural changes produced 
by annealing. It should be remarked that the unannealed bar, Fig. 112, 
(McW. & L.) %-inch diameter when bent over a ^^-inch radius broke at 
43°. After annealing, same bar bent double without fracture. 




after annealing 
Fig. 112. 



f ^H 


EKIF^^''' ^ 


r ^^^V 


*■P^-~--<^.j^ 


^^^ 




i^^S^ 


^^B^^p^R 


^^. 


^^m 


faS^Kj 


pj^Mff^X 


nH^IHBl 


^^^Sbt^^^W '^s^ 


^r^BBl 


^BKrS^^Sir^^ 


m v^OB 


BSOf^^^ 


3ii^— 4^ 



Fig. 113. 



Fig. 113 (McW. & L.) shows the structure of a portion of a large 
open hearth casting, having originally the same structure as the unan- 
nealed part of Fig. 112 after insufficient annealing. When thoroughly 
annealed the structure was as shown in Fig. 114. 

A test bar i inch square as shown in Fig. 113 broke at 40°; while one 



Tropenas Process 401 

as per Fig. 114 bent at 101° without fracture, showing tensile strength of 
33 tons per square inch; elongation 30 per cent; reduction of area 41 
per cent. The composition of the casting was C.C. 0.24, Si 0.15, 
Mn 0.8, P 0.04, S 0.05. 




Fig. 114. 

Other micrographs of most interesting character are shown on pages 
293 to 297 and 338 to 354 (McW. & L.). 

The process of annealing must be varied to suit different compositions 
and purposes for which the steel is provided. 

Tropenas Process 

This process was patented by Alex. Tropenas of Paris in 1891; the 
first converter, 800 pounds capacity, was erected at the works of Edgar 
Allen & Co., Ltd., ShefiQeld, Eng., and introduced into the United States 
in 1898. 

It produces hotter steel than any other process. The steel may be 
carried for considerable distances in hand ladles or shanks and poured 
into small castings. 

The Tropenas process consists in melting a calculated mixture in the 
cupola, transferring the metal to a special type of converter and its 
conversion to steel therein. The reactions are identical with those of 
the Bessemer and open hearth furnaces; the difference lies in the manner 
of producing these reactions. The converter is designed to conserve 
and increase the heat as much as possible and by preventing evolution 
in the bath, to keep out any gases not necessary for or caused by the 



402 



Steel Castings in the Foundry 



decarburization, mechanical disturbance, gyration or ebullition of the 
bath is reduced to a minimum. 

The converter is in general similar to the Bessemer converter, the 
particular difference being in the location and construction of the 
tuyeres. 

Figs. 215 and 216, pages 307 and 308 McW. & L. give fair illustra- 
tions of the device. The operation consists in melting the iron in the 
cupola precisely as for gray iron castings, except that enough for the 
charge must be gathered at the first tapping. The melted iron is then 
transferred to the converter and skimmed clear of slag. The converter 
is so adjusted that the level of the metal reaches exactly to the lower edge 





Fig. 115. 



Fig. 116. 



of the bottom tuyeres, so that the blast will strike exactly upon the 
surface of the metal. The longitudinal axis of the converter should 
make an angle of from 5° to 8° with the vertical. This is a matter of 
importance and extreme care must be taken to obtain the correct position 
before applying the blast. The upper tuyeres are closed and the blast 
turned on with about 3 pounds pressure. 

If the composition of the iron is correct and it has been melted hot, 
sparks and smoke will be emitted from the converter for about four 
minutes, then flame appears which gradually increases in volume and 
brilliancy. After about ten minutes, what is known as "the boil" 
appears. In a few minutes this dies down considerably, and the blow 
remains quiescent for a time. Then the flame increases again, attains 
the maximum brilliancy and finally dies down for the last time. 



• Chemistry of the Process 403 

This is the end of the blow, the carbon, silicon and manganese having 
been reduced to the lowest limits. 

The converter is now turned down, the blast shut off and a weighed 
amount of ferrosilicon, ferromanganese or silicon speigel added to 
recarbonize the steel to the desired point. The steel is now ready for 
casting. On account of its great fluidity and thin slag it may be poured 
over the hp of an ordinary ladle, instead of from one with a bottom pour. 

Claims made for this process. 

1. The form of the bottom of the converter gives a greater depth in 
proportion to the surface area and cubic contents than any other pneu- 
matic process, preventing the disturbance of the bath when blowing. 

2. The symmetrical position of the tuyeres with respect to the center 
tuyere prevents any gyrating or churning of the bath. This is directly 
opposed to all other processes. 

3. The special position of the bottom tuyeres during blowing, so that 
they are never below the surface of the bath, reduces the power necessary 
for blowing; as only enough air Is introduced to make the combustion 
and not to support or agitate the bath. 

4. The oxidation of the metalloids takes place at the surface only, the 
reaction being transmitted from molecule to molecule without any 
mechanical disturbance. 

5. The addition of a second row of tuyeres completely burns the CO 
and H produced by the partial combustion of carbon and the decomposi- 
tion of moisture introduced with the blast and this increases the tem- 
perature of the bath by radiation. 

6. Very pure steel is obtained, as the slag and the iron are not mixed 
together. 

7. There is a minimum of waste on account of the bath being kept 
comparatively quiet. 

8. Less final addition is required on account of the purity of the steel 
and its freedom from oxides. 

Chemistry of the Process 

No fuel is needed in the converter. The increase in temperature after 
the melted metal is introduced is occasioned by the combustion of the 
metalloids during their removal. 

These elements are carbon, siUcon and manganese. The oxidation 
of the siUcon furnishes by far the greatest part of the useful heat. Prof. 
Ledebur has calculated that the rise in temperature of the bath due to 
the combustion of i per cent of each of the constituents is as follows: 
SiHcon 300° C; phosphorus 183° C; manganese 69° C; iron 44° C; 
carbon 6° C. 



404 Steel Castings in the Foundry * 

It is necessary that the composition of the bath before blowing should 
be that which has been found to give the best results. 

Sulphur and phosphorus are as unaffected here as in any other acid- 
hned f lurnace and the content of those elements in the finished steel will 
depend on how much the stock melted contained. 

The cupola mixture generally consists of low phosphorus pig iron and 
steel scrap, composed of runners, risers and waste from previous heats. 
As much as 50 per cent scrap may be carried successfully. The mixture 
must be made in such proportions that the analysis after melting will be: 

Per cent 

Silicon 1 . 90-2 . 25 

Manganese o. 60-1 . 00 

Carbon, about 3 • 00 

The result of low silicon is to make the blows colder; that of high 
silicon to make the blows unduly long and to increase the wear on the 
lining. 

Manganese should be kept w^ithin the limits specified. Low man- 
ganese tends to make the slag thick. High manganese makes the blow 
sloppy and corrodes the lining. 

During the first period of the blow, the silicon chiefly is oxidized and 
the carbon changed from graphitic to combined. The manganese is the 
most active element in the middle of the blow, being most rapidly 
eliminated at the boil. The last period brings the carbon flame, and the 
indications are so plain that it is feasible to stop the blow before all the 
carbon is burned out, thereby reducing the amount of carburiser needed. 
In addition to these elements a certain amount of iron is unavoidably 
oxidized and the total loss of all elements included is about 12 per cent. 

Converter Linings 

The converter is generally lined with an acid or silica lining. Success- 
ful experiments have been made with a basic lining (dolomite), but it has 
not been developed commercially. Special shaped blocks to fit the 
converter or the regular standard shapes may be used. 

The material must be of the highest grade sihca stock, burnt at the 
highest possible kiln temperature. It usually contains from 95 to 97 
per cent Si02, and is practically free from lime and magnesia. 

Another method in frequent use is to run ground ganister around a 
collapsible form. This probably is the cheapest method. Before making 
the first blow, the converter is made white hot by a coke or oil fire. 

Mr. J. S. Whitehouse of Columbus, Ohio, in a paper read before the 
American Foundrymen's Association, states that the claims which were 



Converter Linings 405 

made for the side blow converter, when first introduced into America 
were, to say the least, absurd. Many failures were made by employ- 
ing inexperienced workmen, who had only limited instructions from 
experts sent out with the apparatus and the results were frequently 
disastrous. 

A year's experience, at least, under proper instruction is required before 
a man can become a competent blower. He must be able to tell the 
temperature of the metal soon after the flame starts and to judge the 
siUcon by the first period. He must tell when the blow is finished from 
the slag as well as by the flame. He must know how to keep the lining 
in the best shape to get all the heat possible from the process, and the 
hundred little kinks of the trade, which, as a rule, the expert will never 
impart, but are obtained only from experience. 

A man with the above qualifications will blow with a loss of less than 
17 per cent — about 15 per cent. 

With proper blowing the main loss comes from the silicon in the charge, 
usually 2 per cent, which is oxidized together with iron and manganese 
to form the slag. 

Mr. Whitehouse learned to blow with 2 per cent silicon, but for the 
past few years has been blowing iron, analyzing from 0.90 to 1.25 per 
cent silicon from the cupola, and often has been obliged to use scrap 
while blowing. 

There is an advantage in the increased amount of scrap which can be 
carried, as it cuts down the cupola loss by increasing the amount of 
carbon in the charge. For example: He charges 50 per cent pig carrying 
about 3.75 per cent carbon and 50 per cent scrap having 0.25 per cent 
carbon. Tests from such iron from the cupola give 3.25 to 3.50 per cent 
carbon, showing a gain of 1.25 to 1.50 per cent carbon, taken from the 
coke, instead of purchased in the pig iron. 50 per cent scrap can be 
melted in the cupola, using only i2i/i per cent coke, but the blower must 
have a complete knowledge of cupola practice. Most blowers use too 
much volume and too high pressure of blast to get the best results. With 
low silicon the volume and pressure of blast must be low. No two blows 
will act alike and require different treatment, which can be determined 
by the flame, but which he is unable to describe. 

It is as necessar}^ for the blower to regulate the air valve to get proper 
combustion as it is for the melter to adjust air and gas valves. With 
ordinary care the steel produced in a converter is very uniform in carbon 
and silicon; more so, he thinks, than in the open hearth. The greatest 
variation seems to be in manganese. The temperature of the metal 
and the condition of the slag cause more variation in the converter than 
in the acid open hearth. It is possible to run several weeks without 



4o6 



Steel Castings in the Foundry 



taking an analysis and find at the end of the run very little variation in 
the elements. 

While this is possible with the open hearth, it is not practiced on 
account of the risk. It is, however, frequently done in converter practice. 
The method of making the molds is identical with that followed in the 
open-hearth practice. 




Fig. 117. — Arrangement of the Cupola and Converter. The Metal is 
Handled by a Fovir-ton Pneumatic Jib Crane. 



An ordinary converter shop, with one two-ton converter is capable of 
producing between 100 and 150 tons of good castings per month, blowing 
three times a week. He concludes with saying that the management 
must be good and the salaries paid the officers as reasonable as possible, 
otherwise the shop is fore-doomed to failure, regardless of the quaUty of 
the product. 

At the Cincinnati Meeting of the American Foundrymen's Associa- 
tion, Mr. Whitehouse, in reply to various inquiries, made the following 
statements : 



Converter Linings 



407 



When the flames show that the blow is getting very hot, scrap is 
thrown in at the top of the converter until it cools down. The scrap is 
as small as can be conveniently handled and is not preheated. 

The blast pressure averages from 2.25 to 2.50 pounds. 




Fig. 118. — Pouring the Iron into the Converter before the Blow. 

Sometimes, after the sihcon is reduced and during the blow, steel scrap 
is thrown into the converter. 

The carbon can be varied by the final additions. 

It is usual and customary to blow the heat down till the flame drops; 
the carbon is then about o.io per cent. The carbon is then raised by the 
addition of melted pig iron or pulverized coke. The carbon can be 
raised as much as desired. If more than 0.40 or 0.50 per cent carbon is 



4o8 



Steel Castings in the Foundry 



required, the blow is stopped before completion. It is customary to 
blow down to .09 or o.io per cent carbon, then to recarbonize with ferro- 
manganese, melted pig iron and spiegeleisen. I usually use coke. If 
ferromanganese is melted in a small cupola, as has been done in the East, 
the loss is very heavy. The most economical practice is to throw the 
ferromanganese into the converter at the end of the blow. The usual 
custom is to add ferromanganese and then pig iron. 

"My practice is never to reline entirely. At the end of the heat day, 
the converter is cooled off, patched up, dried out and is then ready for 
_ the next day. Where the converter is 

used until it is cut out, the Uning re- 
moved and then renewed, there is a great 
loss of iron." 

The practice is to blow just at the sur- 
face, with the blast impinging slightly on 
the metal. During the blow the tuyeres 
are submerged, and if the pressure is sud- 
denly stopped for any cause the iron. wiU 
run into the wind box. The converter is 
so placed that the blast will strike the 
surface of the metal at an angle of 175** 
to 171°. He does not use a second row 
of tuyeres. Upon starting to use the 
converter, there was an upper row of 
tuyeres, but they were subsequently dis- 
carded. The lower tuyeres furnish all 
the blast required. 

Formerly he used bull ladles in pour- 
ing small castings and experienced no 
trouble. At the present time, the entire 
heat, sometimes consisting of castings 
weighing less than thirty pounds, is poured with a thousand-pound 
ladle. 

The following extract is from the Foundry, Jan., 19 10, describing the 
equipment of the recently erected steel foundry of the Vancouver En- 
gineering Works, Ltd., Vancouver, B.C. 

The cupola is the Standard Whiting type, having a rated capacity of 
six to seven tons per hour. 

Iron is tapped from the cupola into a six-thousand-pound ladle, carried 
by a pneumatic crane. Two taps are made to obtain a full charge for 
the converter. 
The composition of the iron is as follows: Si. 1.80 to 2.00; S. 0.04; 




Fig. 119. — View of One End of 
the Foundry, Showing the Con- 
verter Discharging Steel into a 
Ladle. 



Standard Specifications for Steel Castings 



409 



Phos. 0.04; Mn. 0.60 to 1.50. The cupola charge is so proportioned as to 
give about one per cent manganese. Steel scrap is available as desired. 

The converter, of two-tons capacity, 
is of the standard Whiting type (Tro- 
penas) and is lined with ganister, sand 
and fireclay. This lining, if cared for, 
will give from 180 to 200 blows. The 
air pressure of blast to converter ranges 
from three to five pounds per square 
inch, regulated by valve on operator's 
platform. 

The blowing operation requires from 
15 'to 20 minutes, varying with the 
percentage of metalloids in the iron. 
The temperatiure of the bath depends 
upon the rapidity of the blow. 




Fig. 



120. — The Converter in 
Operation. 

Reduction in the weight of metal is about 18 per cent. 
The steel comes from the converter at 1700° C, insuring sufficient 
fluidity to give sharp, sound castings of light section. 



Standard Specifications for Steel Castings Adopted 
BY American Association for Testing Materials 
Process of Manufacture 

1. Steel for castings may be made by the open hearth, crucible or 
Bessemer process. Castings to be annealed or unannealed a& specified. 

Chemical Properties 

2. Ordinary castings, those in which no physical requirements are 
specified, shall contain not over 0.40 per cent carbon, nor over 0.08 per 
cent of phosphorus. 

3. Castings which are subject to physical test shall contain not over 
0.05 per cent of phosphorus, nor over 0.05 per cent of sulphur. 

Physical Properties 

4. Tested castings shall be of three classes, hard, medium and soft. 
The minimum physical qualities required in each class shall be as foUows: 



Properties 


Hard 
castings 


Medium 
castings 


Soft 
castings 


Tensile strength, pounds per inch 

Yield point, pounds per inch 

Elongation per cent in 2 inches 


85,000 

38,250 

15 

20 


70,000 

31.500 

18 

25 


60,000 

27,000 

22 







4IO 



Steel Castings in the Foundry 






5. A test to destruction may be substituted for tensile test in the case 
of small or unimportant castings, by selecting three castings from a lot. 
This test shall show the material to be ductile, free from injurious defects, 
and suitable for the purposes intended. 

A lot shall consist of all castings from the same melt, or blow annealed 
in the same furnace charge, 

6. Large castings are to be suspended and hammered all over. No 
cracks, flaws, defects, nor weakness shall appear after such treatment. 

7. A specimen one inch by one-half inch (i " X v/') shall bend cold 
around a diameter of one inch (i") without fracture on outside of bent 
portion, through an angle of 120° for the "soft," and 90° for "medium" 
castings. 

Test Pieces and Methods of Testing 

8. The standard turned test specimen, one-half inch {W) diameter 
and two inch (2") gauged length, shall be used to determine the physical 
properties specified in paragraph No. 4. It is shown in the following 
sketch. 

9. The number of standard 
test specimens shall depend 
upon the character and im- ' 
portance of the castings. A 
test piece shall be cut cold from 
a coupon to be molded and cast 
on some portion of one or more 
castings from each blow or melt, or from the sink heads (in case heads 
of sufl&cient size are used). The coupon, or sink head, must receive 
the same treatment as the casting, or castings, before the specimen is 
cut out and before the coupon, or sink head, is removed from the 
casting. 

10. One specimen for bending test, one inch by one-half inch (i" X 
W) shall be cut cold from the coupon, or sink head, of the casting, or 
castings, as specified in paragraph No. 9. The bending test may be 
made by pressure or by blows. 

11. The yield point specified in paragraph No. 4 shall be determined 
by careful observation of the drop of the beam, or halt in the gauge of 
the testing machine. 

12. Tiu-nings from the tensile specimen, drillings from the bending 
specimen or drillings from the small test ingot, if preferred by the in- 
spector, shall be used to determine whether or not the steel is within 
the limits, in phosphorus and sulphur, specified in paragraphs Nos. 2 
and 3. 



41 



■11 



2i"- 



-Mi"k- 






Fig. 



Open-Hearth Methods for Steel Castings 411 

Finish 

13. Castings shall be true to pattern, free from blemishes, flaws or 
• shrinkage cracks. Bearing surfaces shall be solid, and no porosity shall 

be allowed in positions where the resistance and value of the casting 
for the purpose intended will be seriously affected thereby. 

Inspection 

14. The inspector, representing the purchaser, shall have all reasonable 
facilities afforded him by the manufacturer to satisfy himself that the 
finished material is furnished in accordance with these specifications. 

All tests and inspections shall be made at the place of manufacture, 
prior to shipment. 

The following paper, by Mr. W. M. Carr, on the manufacture of steel 
castings in small quantities by the open-hearth process is given herewith 
in full. 

Open-Hearth Methods for Steel Castings 

With Remarks on the Small Open-Hearth Furnace 
By W. M. Caer, New York City 

It is a fact that the open-hearth process for the manufacture of steel 
is gradually gaining ground, as can be proved by statistics. The reason 
for its supplanting other methods is mainly one of quality. Further, the 
basic open-hearth process permits a mixture of pig iron and miscellaneous 
steel scrap of a lower grade and cheaper price than raw material necessary 
to other processes. 

With the foregoing facts in mind the author presents this article for 
the consideration of prospective investors in the manufacture of steel 
castings in small, moderate and large tonnages; to be more explicit, 
small tonnages are capacities of melting units in one-half, one and two 
tons per heat. Moderate tonnages are capacities of furnaces of two to 
five tons per heat, and large tonnages are capacities from ten to twenty- 
five tons per heat. There are thus offered possible outputs to meet 
almost any requirements. 

In presenting the claims, it is with the recognition of the following 
advantages : 

1. The small capacity furnaces cost less to install than any other 
steel making devices excepting only crucible melting furnaces. 

2. The economy in operation of open-hearth furnaces in any capacity 
over that of any other steel-making process. 

3. The certainty of results, the greater degree of control in operation 
and the reduction of the personal equation to the lowest possible expres- 
sion. 



412 



Steel Castings in the Foundry 



It is generally known to the foundrymen that the largest production 
of steel castings comes through open-hearth furnaces of capacities of 
j&ve to twenty-five tons per heat. Such practice is established and 
requires constant demand to be profitable, and investment of consider- 
able capital varying with the size of the plant. It has been thought that 
capacities of less than five tons per heat are not possible by open-hearth 
methods, and engineers generally have dissuaded those who wish to 




Fig. 122. 

engage in the manufacture of steel castings either for their own con- 
sumption or the trade from using open-hearth methods, since up till 
quite recently the tendency has been rather to increase the capacity of 
the open hearth, supposedly for economical reasons rather than to build 
small units with less capacities. 

The author, however, has had the opportunity to demonstrate the 
possibilities of the miniature open hearth and has found from actual 
practice that it is economical, and comparing operation costs with stand- 



Open-Hearth Methods for Steel Castings 413 

ard capacity furnaces, bears equally well in economy. This fact is 
somewhat of an innovation, but nevertheless true, and it can be said 
that the operating cost of the miniature open hearth is less than that 
of any type of steel-producing unit or process, making steel in equal 
quantity. 

To assist those who may not be famihar with an open-hearth furnace 
and its operation, a study of the diagram herewith, (Fig. 122) given may 
be instructive. The upper part of the furnace is represented in sectional 
elevation. The structure is built of refractory bricks and boiuid se- 
curely with structural steel beams and plates at certain points not 
shown in the diagram. The lower part of the furnace, usually below 
the charging floor level or carried below the shop level, consists of the 
chambers, connecting flues leading to a reversing valve and thence to a 
regenerator stack. Referring again to the main body of the furnace it 
will be noticed that the hearth, which is practically a shallow dish lined 
with "siKca" sand is fused into one sohd mass at a high temperature at 
the time of what is known as "making bottom." This is the laboratory 
where the raw material is melted and refined to steel of any desired 
composition. In outhne the practice is as follows and refers to the opera- 
tion of a miniature open hearth fired with fuel-oil being recommended 
in preference to producer gas in capacities of less than five tons per 
heat. 

After the furnace has been brought up to a working temperature — 
white heat — a mixture of acid pig iron and low phosphorus steel scrap 
usually in the proportions, one-third pig and two-thirds scrap, is charged 
into the furnace, adding the pig iron first, and when that becomes 
molten, following with the scrap. The whole mass subsequently becomes 
liquid by means of the oil flame passing above it. At this stage the 
temperature of the furnace has been lessened through the addition of 
the cold stock, but it will still be at a temperature above that required 
to melt pig-iron. But in order to elevate the temperature above that 
required to melt steel and have it in condition to pour, the advantage 
of the principle of regeneration is available. This consists in returning 
to the furnace waste heat which in other types of furnaces escapes to the 
stack. Without a system of regeneration it is not possible to reach a 
proper steel casting temperature ; that is to say, a reverberatory furnace 
without regeneration gives a temperature, (where the combustion of the 
fuel is supported by cold air) , less than that required to properly liquefjj 
steel, but with the principle of regeneration applied to such a furnace, 
high temperatures are readily reached. 

To imderstand this principle we will foUow the course of the flame of 
the burning oil as indicated by the arrows in the diagram. Begirming 



414 Steel Castings in the Foundry 

at the right hand end oil is deHvered to the burner which is shown 
surrounded with a water cooled casing to protect the burner fittings. 
The oil is deHvered either by gravity or pump pressure, but before 
reaching the end of the burner it is atomized or vaporized by air under 
pressure. This air is designated as primary air and performs httle or 
no part in supporting combustion of the oil vapor, and the quantity of 
air delivered in excess above the amount necessary to promote combus- 
tion of the oil is known as secondary air. The secondary air enters the 
reversing valve shown at the stack connection, passes through the right 
hand regenerator, enters the uptakes below the water cooled burner 
casing, performs its function and passes along the roof of the furnace, in 
part, and the remainder, mixed with the products of combustion with 
the strata of flame plajang above the bath, enters the downtake at the 
left hand end of the furnace and in its passage to the stack gives up 
the major portion of its heat to a large quantity of brick work piled 
within the chamber. When the waste gases have passed through the 
reversing valve and entered the stack they have just about enough heat 
to induce the necessary draft. Now, after an interval of twenty to 
thirty minutes the right hand burner may be shut ofl", but not withdrawn 
from the furnace; the reversing valve is thrown and the oil and primary 
air turned on at the left hand end of the furnace. The secondary air 
will then be diverted by the reversing valve to flow through the left hand 
regenerator or checker chamber, and passing through innumerable pas- 
sages in that set of checkers absorbs a large quantity of heat radiating 
from the glowing bricks which became heated in the first instance by the 
outgoing gases during a previous cycle of operation. This radiated heat 
regenerating the secondary air will be added to the temperatiure gener- 
ated by the burning fuel and the products of combustion will accordingly 
have an increased quantity of heat to impart to the checker work at 
the outgoing or right hand end. In other words, whatever temperature 
may be carried in by the secondary air will be equivalent to an increase 
in efficiency of the burning fuel. Successive reversals of the fuel, pri- 
mary and secondary air produce constantly increasing increments in 
flame temperatures below the melting points of the refractory brick 
works. 

We have seen what can be accomplished by storing up and restoring 
to the furnace waste heat from the products of combustion, producing 
4he effect of a higher possible temperature than in any type of melting 
furnace. In addition to this effect another one is quite active and that 
is reflection of heat from the walls and roof of the furnace upon the surface 
of the bath of metal. This latter effect, known as radio-activity, is more 
pronounced in a narrow melting chamber than in a wider one and conse- 



Open-Hearth Methods for Steel Castings 415 

quently the result will be two factors, one a decreasing fuel consumption 
and the other the possibihty of superheating steel in a miniature open- 
hearth. This fact has not been recognized heretofore because most open- 
hearth furnaces are fired with producer gas, and since that fuel requires 
pecuKar furnace construction to get the best results in burning it, it has 
not been found possible to make use of such fuel in a comparatively short 
furnace hearth and therefore all furnaces designed to use that fuel must 
have a comparatively long hearth tending mainly in the direction of 
increased capacities rather than decreased. On the other hand, the length 
of the hearth is not restricted where oil can be substituted for producer 
gas and therefore it has been found possible to operate an open-hearth 
furnace as small as 350 pounds capacity per -heat. Thus a new field is 
opened to make steel by the open-hearth process. 

Referring again to the operating method, we saw where the bath of 
metal was molten and at a moderate temperature. This temperature 
was due to the fact that the metal was highly carburized, since the 
presence of carbon lowers the melting point of iron. We saw how it was 
possible to gradually increase the temperature of the fiu-nace by the 
regeneration of the secondary air, and with that constant elevation of 
temperature, dormant chemical actions will be set up. The first effect 
will be an oxidization of the siHcon occurring mostly on the surface of 
the metal by the oxidizing action of the flame. The product would be 
sihca, which combines with whatever oxide of iron might be present in 
the bath of metal. The combination would form a slag of comparatively 
Ught weight that would rise to the surface and cover the bath. The slag 
is shown in the diagram by the heavy black Hne. This layer of slag 
prevents the metal below from direct contact with the flame. After the 
removal of the silicon the next action will be the removal of the carbon. 
This action is a gas-forming one and wiU cause a bubbling or boil through- 
out the bath. The action can be augmented from time to time by the 
addition of iron oxide in the form of iron ore. As the decarburization 
progresses test plugs are taken from time to time, the operator judging 
the amount of carbon in the bath by their fracture and malleability. 
When the carbon has decreased to a predetermined point, the boil may 
be stopped or killed by deoxidizing agents such as ferrosilicon and ferro- 
manganese in properly weighed amounts. The metal can then be trans- 
ferred to molds. This method as outhned refers to the acid process. 
In it the elements sulphur and phosphorus are not removed. The basic 
process consists of a hearth hning made of magnesite. Such a hning 
permits an addition of hmestone to form a slag which will absorb the two 
elements and make a purer steel, chemically speaking, than the acid 
process, and at the same time allow the use of cheaper and irregular 



4i6 Steel Castings in the Foundry 

raw materials against the acid process with strictly limited chemical 
composition concerning the two elements mentioned. 

With open-hearth furnaces designed to use producer gas and which 
rarely go below five tons capacity it is not possible to adapt them to 
intermittent operation. Even in the smaller producer-gas fired furnaces 
the roof span is considerable, resulting in heavy stresses on the side walls. 
These stresses will vary as the furnace is heated and cooled, and if such 
alternations are frequent there is danger of collapse of the furnace. It 
becomes necessary then to maintain them continuously at a steady tem- 
perature. Unless there should be demand for regular tonnage the fuel 
consumption during idle periods would be a constant expense. 

In miniature open-hearth furnaces, owing to the comparatively narrow 
hearth chamber, the roof span is of course lessened and therefore v/hat- 
ever expansion or contraction therein following heatings and coolings, 
wiU result in comparatively slight stresses, and these results decrease in 
effect with the lessened capacity furnaces, and they therefore lend 
themselves to intermittent operation with greater ease and lessened 
liabihty of repairs. The miniature open hearth is most satisfactory in 
the roUing type with the body cylindrical, so that the stresses even 
though slight will be evenly distributed, whereas in a rectangular -form 
the roof will always rest and thrust upon the inside walls. In fact the 
miniature open hearth is not recommended to be built in the stationary 
type. 

In conclusion the miniature open hearth is not costly to install, is 
comparatively simple to operate, gives results equal to standard open- 
hearth practice, makes hotter steel than the regular open hearth and . 
can show costs equally as low per poimd of molten metal in the ladle. 



Comparative Cost of Steel made by Different Processes 417 

Comparative Cost of Steel made by DiSerent 
Processes 

From paper presented to the American Foundrymen's Association 
by Mr. Bradley Stoughton. 

Table I. — Acid Open Hearth 



Raw materials 



Pig iron 

Heads, gates, etc 

Foreign scrap 

Defective castings* (account bad metal) 
Ferro-alloys 

Total metal 

Operating costs 

Cost of steel in ladle 



Per 2000 pounds of steel in ladle 



Price 

of raw 
materials 
per 2000 
pounds 



$14.00 
14.00 
14.50 
50.00 
40.60 



Weight 
used, 
pounds 



300 
660 
1080 
20 
29 
2089 



Per cent 
used 



Cost 



$2. 10 

4.62 

7.83 

.50 

^ 

$15.64 

5.5ot 

$21.14 



Cost 



$15.64 
8.85 t 
$24.49 



Cost of Steel in Castings 








Cost of steel in ladle -^ 65 per cent J = 
Less credit for heads, etc., as_scrap = . 








$32.52 
4.62 

$27.90 


$37.68 








4.62 








$33.06 













* The price given for defective castings is over and above their value as scrap 
See the text following for further discussion of this charge. 

t The charge of S5.50 for operating costs is the figure for a 2S-ton furnace and large 
tonnage; that of $8.85 is for a small furnace and small production. 

t Of the steel in the ladle, 65 per cent goes into castings, 33 per cent goes into heads, 
gates, etc. and 2 per cent is lost in spattering, etc. 



4i8 



Steel Castings in the Foundry 
Table II. — Basic Open Hearth 



Raw materials 



Pig iron 

Heads, gates, etc. . . . 

Foreign scrap 

Defective castings*. . 
Ferro-alloys 

Total metal 

Operating costs . . 
Cost of steel in ladle. 



Per 2000 pounds of steel in ladle 



Price 

of raw- 
materials 
per 2000 
pounds 



$12.75 
14.00 
II. 15 
SO. 00 
40.60 



Weight 
used, 
pounds 


Per cent 
used 


Cost 


1040 


52 


$6.63 


660 


33 


4.62 


350 


17 ^i 


1.9s 


40 


2 


1. 00 


33 


1I/2 


.67 


2123 


106 


$14.87 
6. lot 
$20.97 



Cost 



$14.87 
9 -55 ! 

$24.42 



Cost of Steel in Castings 



Cost of steel in laddie H- 65 per 
cent J — 








$32.26 
4.62 

$27.64 


$37.57 
4 62 


Less credit for heads, etc. as scrap = . 








Net cost of steel in castings . ... 








$32.95 













* See footnote under Hearth, Table I. 
t See footnote under Table I. 

t Of the steel in the ladle, 65 per cent goes into castings, 33 per cent goes into heads, 
gates, etc., 2 per cent is lost in spattering in pouring. 



Acid Open Hearth and Basic Open Hearth 



419 



Acm Open Hearth and Basic Open Hearth 
[When Together in One Plant] 



Raw materials 


Acid open hearth per 

2000 pounds of steel 

in ladle 


Basic open hearth per 
2000 pounds of steel 
in ladle 


Price of 

raw materials 

per 2000 

pounds 


M 




8 






h 


1 




$14.00 

14.00 
14.50 
50.00 
40.60 


300 

1320 

420 

20 

29 


15 

66 
21 

I 
I 

104 


$2.10 

9.24 

3.05 

.50 

■ 59 


$12.75 
II. 15 

so. 00 
40.60 


1040 

lOIO 

40 

33 
2123 


52 

'151/2 
2 
11/2 


$6.63 


Heads, gates, etc., from 




5.63 




Ferroalloys 


.67 


Total metal 




2089 


$15.48 

5.50 

$20.98 




71 


$13.93 

6.10 

$20.03 


Operating costs 

Cost of steel in ladle 




Cost of Steel 


in Castings 




Cost of Steel in Castings 


Cost of steel in ladle -h 65 pe 






$32.28 

4.62 

$27.66 









$30.81 








4.62 








$26 . 19 











420 



Steel Castings in the Foundry 
Table IV. — Converter 





Per 


2000 pounds of steel in ladle 


Raw materials 


Price 

of raw 

materials 

per 2000 

pounds 


Weight 
used, 
pounds 


Percent 
used 


Cost 


Cost 


Pig iron 


$14.00 
17.40 
14.00 
80.00* 
40.60 


300 

1280 

660 

20 

35 

229s 


15 
64 
33 

It 

2 

115 


$2.10 
II. 14 
4.62 
.8ot 
.71 

$19.37 
3. sot 

$22.87 




Pig iron 




Heads, gates, etc. 




Defective castings (account bad metal) 
Ferroalloys . . 




Total metal 


$19-37 






Cost of steel in ladle 




$24.87 









Cost of Steel in Castings 











$35.18 
4.62 

$30.56 


$38.26 










4.62 


Net cost of steel in castings . . . . 








$33.64 











• See footnote under Table I. 

t The percentage of defective castings in converter practice will actually be less 
than this, so that the cost is a little higher than justice to average converter practice 
demands. In the absence of average figiures, we have charged it the same as acid 
open hearth, with this correction. 

t Operating cost, $3-5o, is for one 2-ton converter making 150 tons per week. The 
$5-50 per ton is a 2-ton converter with small production. 



Converter, with Large Waste 421 

Table V. — Converter, with Large Waste 





Per 2000 pounds of steel in ladle 




Raw materials 


Price 
of raw- 
materials 
per 2000 
pounds 


Weight 
used, 
pounds 


Per cent 
used 


Cost 


Cost 


Pig iron .... 


$14.00 
17.40 
14.00 
80.00 
40.60 


300 
1360 

660 

20 

_^ 

2378 


IS 

68 

33 

I 

2 

119 


$2.10 

11.83 

4.62 

.80 

.77 

$20.12 

3.50 

$23.62 




Pig iron 




Heads, gates, etc. 




Defective castings account bad metal. 




Total metal 


$20.12 






5.50 


Cost of steel in ladle 




$25.62 









Cost of Steel in Castings 



Cost of steel in ladle -^ 65 per cent . 

Less credit for heads, etc., as scrap. 

Net cost of steel in castings 



$36.34 
4.62 

$31.72 



$39-42 
4.62 

$34.80 



422 Steel Castings in the Foundry 

Table VI. — Acm Open Hearth [Making Small Castings] 



Raw materials 



Pig iron 

Heads, gates, etc 

Foreign scrap 

Defective castings account bad metal, 
Ferroalloys 

Total metal 

Operating costs 

Cost of steel in ladle 



Per 2000 pounds of steel in ladle 



Price 
of raw- 
materials 
per 20CX) 
pounds 



S14.00 
14.00 
14.50 
50.00 
40.60 



Weight 

used, 

pounds 



300 

660 



120 
29 



Per cent 
used 



Cost 



$2.10 
4.62 
7. II 
300 

^ 

$17-42 

5.50 

$22.92 



Cost 



$17-42 

8.85 

$26.27 



Cost of steel in castings 



Cost of steel in ladle -f- 65 per cent*. 

Less credit for heads, etc., as scrap. . 

Net cost of steel in castings 



$35.26 

4.62 

$30.64 



S40.41 
4.62 

$35.79 



* Of the steel in the ladle, 65 per cent goes into castings, 33 per cent goes into heads, 
gates, etc., 2 per cent is lost in spattering during pouring. In making small castings, 
the loss in pouring from a bottom-poured ladle would be much larger than this, and 
the cost of steel in castings would be increased $1 to $3 per ton, but data is lacking 
for exact estimates. 



Crucible Castings 



423 



Table VIL — 


Basic Open Hearth [Making Small Castings] 




Per 


2000 pounds of steel in 
ladle 


Per 2000 pounds of 
steel in ladle 


Raw materials 


Price of 

raw materials 

per 2000 

pounds 


13 

li 




S 


1 











5 




$12.75 
14.00 
II. IS 
50.00 
40.60 


1040 
660 
190 
200 

33 


52 
33 

10 

1I/2 


$6.63 

4.62 

1.06 

5.00 

.67 


$17.98 
9-55 


1040 

660 
350 
300 

33 


52 

33 

17I/2 
15 

1 1/2 


$6.63 

4.62 

1.95 

7.50 

.67 




Heads, gates, etc. . . . 

Foreign scrap 

Defective castings . . . 








Total metal 

Operating costs . . 


2123 


106 


$17.98 
6.10 


2124 


106 


$19.93 
6.10 


$19.93 
9.55 


Cost of steel in ladle.. 




$24.08 


$27.53 


$26.03 


$29.48 



Cost of Steel in Castings 



Cost of steel in ladle -j- 65 per cent . 

Less credit for heads, etc., as scrap 

Net cost of steel in castings 



$37.05 
4.62 



$32.43 



$42.35 
4.62 



$37.73 



$40.05 
4.62 



$35.43 



$45.85 
4.62 



$40.73 



Table VIII. — Crucible Castings 








Per 2000 pounds steel in ladle 


Raw materials 


Price of 

raw materials 

per 2000 

pounds 


to OQ 

It 




1 




1. 

^ p. 

1 




1 






$25.50 
14.50 
14.00 

125.00 
40.60 


1360 

"660' 
10 
12 


68 

33 

V2 

102 


$17.34 

■■4;62 
.63 

.24 

$22.83 
35.00 

$57.83 


1330 

660 

10 

12 


33 

lOOl/i 




Foreign steel scrap — 

Heads, gates, etc '. 

Defective castings 

Ferroalloys 


$9.64 

4.62 

.63 

.24 


Total metal 

Operating costs . . . 
Cost of steel in ladle.. 


2042 


2012 


$15.13 
35.00 

$50.13 



Cost of Steel in Castings 



Cost of steel in ladle -f- 66 per cent* $87.62 

Less credit for heads, etc. , as scrap 4 . 62 



Net cost of steel in castings $83 .00 



$75.95 
4.62 



$71-33 



* Of the steel in the ladle, 66 per cent goes into castings, 33 per cent goes into heads, 
gates, etc. and i per cent is lost in poiiring. 



424 



Steel Castings in the Foundry 
Table IX. — Electric Furnace 



Raw materials 



Steel scrap 

Heads, gates, etc.. 
Defective castings. 

Ferroalloys 

Total metal... 



Per 2O0O pounds of steel in ladle 



Price 

of raw 

materials 

per 2000 

poimds 



$9.50 
14.00 
125.00 
40.60 



Weight 

used, 

pounds 



1330 

660 

10 

12 

2012 



Per cent 
used 



661/i 
33 

looH 



Cost 



Cost of netting steel 




In ladle 



Electric power at i cent per kilowatt hour 
" " " 2 cents '* " " 

" " 3 " *' " 

• 4 " " " 

• 5 ' 



$39.03 
52.89 
66.76 
80.62 
94.49 



CHAPTER XVIII 
FOUNDRY FUELS (Cupola) 

The fuels available for melting iron in the cupola are anthracite coal 
and coke. 

Anthracite Coal 

Lehigh lump is the best coal for the purpose. It produces a hot iron 
and melts it rapidly. On account of the cost as compared with coke, it 
is now Uttle used in districts removed from the anthracite region. 

A mixture of anthracite and coke, particularly for the bed, gives most 
excellent results, especially for prolonged heats. 



Coke 

When bituminous coal is exposed to a red heat for a prolonged period 
with total or partial exclusion of air, the volatile matter is driven off and 
the residuum is coke, containing more or less impurities. The coal used 
is of the coking variety and to produce good foundry coke should be low 
in sulphur and ash. Seventy-two hour Bee Hive Coke is most generally 
used by foundrymen. This has a hard, cellular, columnar structure, 
with a gray, silvery surface. The smooth, glistening appearance iound 
in much of it is due to quenching in the furnace. (Weight about 25 
pounds to cubic foot.) There will be found in each carload of coke 
"black-tops" and "black-butts"; the appearance of the former is due 
to deposits of carbon from the imperfect combustion of the gases at the 
top of the furnace. They in no way affect the value of the fuel. Black 
butts, however, come from incomplete burning and contain unconverted 
coal. These should be accepted only in limited quantities. 

The following are analyses from different sections: 



Localities 


Fixed 
carbon 


Volatile 
matter 


Moisture 


Ash 


Sulphur 




89. 58 
92.58 
80. SI 
92.38 
87.29 


.46 

.49 

1. 10 


.03 
.20 
.45 


9. II 
6.05 

16.34 
7.21 

10.54 


.81 




.68 


Chattanooga. ". 

New River. 


1.59 
.56 


Birmingham 


1. 19 







425 



426 Foundry Fuels 

Specific gravity averages 1.272. Coke will absorb from 10 to 30 per 
cent of its weight in moisture, depending on exposiu-e. After exposure 
to a hard storm the increase in weight may easily be 15 per cent. 

Less pressure of air, more volume and larger tuyere area are required 
when melting with coke than with anthracite coal. 

The following specifications for coke from the J. I. Case Co. are given 
by Mr. Scott. 

Gk)od clean 72-hour coke, massive and free from granulation, dust and 
cinder. Per cent 

Moisture not over i . 50 

Volatile matter not over 3 . 50 

Fixed carbon not under 86 . 00 

Sulphur not over 0.75 

Ash not over 11 . 50 

Coke which has over 0.85 sulphur, 0.05 phosphorus, less than 85 
fixed carbon or less than 5.00 ash will be rejected. 
I Good foundry coke should be high in carbon, low in sulphur, have 
good columnar structure, and there should not be a large percentage of 
small pieces in a carload. The product should be uniform. 

By-Product Coke 

Certain chemical works, in the distillation of bituminous coal for 
ammonia, manufacture coke as a by-product. This, when especially 
prepared for foundry purposes, gives excellent results. It is darker, 
harder and more irregular in form than beehive coke. It is high in 
carbon and low in sulphur, makes a very hot fire and will melt more 
iron than an equal weight of beehive. The short description of the 
process of making this coke by Mr. W. J. Keep is given herewith. 

"The retort oven is a closed chamber from 15 to 24 inches in width, 
5 to 8 feet in height and from 25 to 45 feet long. From 25 to 50 of these 
ovens are placed in a battery. 

"The coal is charged through three or more openings in the top and 
levelled off to within a foot of the roof, after which the oven is carefully 
closed and sealed, in order to exclude the air. The oven is heated by a 
portion of the gas driven off in the process of coking. This is not burned 
in the oven itself, but in flues constructed in their walls. The heat is 
conducted through the walls of these combustion flues to the charges of 
coal and distillation thereof is started immediately. 

"The gas which is driven off is conducted through an apparatus in 
which the tar and ammonia are recovered; after which a portion of the 
gas is returned to be burned in the oven flues, and the balance disposed 
of as local conditions determine. 



Effect of Atmospheric Moisture upon Coke 427 

"Distillation proceeds from the side walls toward the middle of the 
oven and the gas is probably driven toward the center of the oven, where 
it rises, forming a cleavage plane the whole length of the oven. When 
the process is completed, which takes place in from 20 to 36 hours, 
depending upon the width of the oven and the temperature maintained, 
the whole charge is pushed out by a steam or electric ram and is immedi- 
ately quenched. The oven is at once closed and, without any loss of 
heat from the oven itself, is again charged with coal. 

"On account of the cleavage plane through the center of the charge, 
no piece of coke can be longer than half the width of the oven." 

"Owing to the complete exclusion of air, there is no combustion in the 
oven; and as the temperature of the oven, when the coal is charged, is 
very high, there is a considerable decomposition of volatile matter with 
consequent deposition of carbon upon the coking charge. As a result 
the yield of coke is a little higher than the theoretical yield, as cal- 
culated from the analysis of the coal. Quenching the coke outside the 
ovens mars its appearance somewhat, destroying its bright, silvery 
lustre, but probably results in carrying off an appreciable quantity of 
sulphur." 

" Coke made from the same coal will have a slightly higher percentage 
of fixed carbon and a slightly lower percentage of ash than if made in a 
retort oven." 

" The quality of retort oven coke depends upon the skill of the operator, 
upon the method of preparing the coal and more than all, upon the 
quality of the coal used. 

He further says that after having satisfied himself that it was good 
coke, "in spite of its very bad appearance," by the use of several car- 
loads, "from that time to this we have never had a pound of other 
coke. All through 1902 the coke was so uniform and satisfactory that 
we melted 9 pounds of iron with i pound of coke." 

EfEect of Atmospheric Moisture upon Coke 

Under normal conditions, at a temperature of 70° F., 1000 cubic feet 
of air, equal in weight to about 75 pounds, contains i pound of moisture. 
Each pound of moisture requires the use of o.io additional pounds of 
coke. Therefore, every additional i.o per cent to the moisture of the 
atmosphere requires 0.03 additional pounds of coke to melt one ton of 
iron. 

From 20 to 40 per cent of the sulphur in the coke is taken up by the 
iron in melting. This may be largely reduced by the liberal use of 
limestone. 



428 Foundry Fuels 

Specifications for Foundry Coke Suggested by 
Dr. Richard Moldenke 

Coke bought under these specifications should be massive, in large 
pieces and as free as possible from black ends and cinders. 

Sampling 

Each carload or its equivalent shall be considered as a unit, and 
sampled by taking from the exposed surface at least one piece for each 
ton, so as to fairly represent the shipment. These samples, properly 
broken down and ground to the fineness of coarse sawdust, well mixed 
and dried before analysis, shall be used as a basis for the payment of the 
shipment. In case of disagreement between buyer and seller an indepen- 
dent chemist, mutually agreed upon, shall be employed to sample and 
analyze the coke, the cost to be botne by the party at fault. 

Base Analysis 

The following analysis, representing an average grade of foundry coke 
capable of being made in any of the districts supplying foundries, shall 
be considered the base, premiums and penalties to be calculated thereon 
as determined by the analysis on an agreed base price: 

Volatile matter i . 00 Ash 12 . 00 

Fixed carbon 85 . 50 Sulphur i . 10 

Penalties and Bonuses 

Moisture. — Payment shall be made on shipments on the basis of 
"dry coke." The weight received shall, therefore, be corrected by 
deducting the water contained. (Note. — Coke producers should add 
sufficient coke to their tonnage shipments to make up for the water 
included, as shown by their own determinations.) 

Volatile Matter. — For every 0.50 or fraction thereof, above the i.oo 
allowed, deduct . . cents from the price. Over 2.50 rejects the shipment 
at the option of the purchaser. 

Fixed Carbon. — For every i.oo or fraction thereof, above 85.50 add, 
and for every i.oo or fraction thereof below 85.50, deduct . . cents. 
Below 78.50 rejects the shipment at the option of the purchaser. 

Ash. — For every 0.50 or fraction thereof below 12.00, add, and for 
every 0.50 or fraction thereof above 12.00 deduct . . cents from the price. 
Above 15.00 rejects the shipment at the option of the purchaser. 

Sidphur. — For every o.io or fraction thereof below i.io add, and for 
every o.io or fraction thereof above, deduct . . cents from the price. 
Above 1.30 rejects the shipment at the option of the purchaser. 



Fluxes 429 

Shatter Test 

On arrival of the shipment the coke shall be subjected to a shatter 
test, as described below. The percentage of fine coke thus determined, 
above 5 per cent of the coke, shall be deducted from the amount of coke 
to be paid for (after allowing for the water) , and paid at fine coke prices 
previously agreed upon. Above 25 per cent fine coke rejects the ship- 
ment at the option of the purchaser. Fine coke shall be coke that passes 
through a wire screen with square holes 2 inches in the clear. 

The apparatus for making the shatter test should be a box capable 
of holding at least 100 pounds coke, supported with the bottom 6 feet 
above a cast-iron plate. The doors on the bottom of the box shall be 
so hinged and latched that they will swing freely away when opened and 
win not impede the fall of the coke. Boards shall be put around the 
cast iron plate so that no coke may be lost. 

A sample of approximately 50 pounds is taken at random from the 
car, using a iH inch tine fork, and placed in the box without attempt to 
arrange it therein. The entire material shall be dropped four times upon 
the cast iron plate, the small material and the dust being returned with 
the large coke each time. 

After the fourth drop the material is screened as above given, the 
screen to be in horizontal position, shaken once only, and no attempt 
made to put the small pieces through specially. The coke remaining 
shall be weighed and the percentage of the fine coke determined. 

If the sum of the weights indicates a loss of over i per cent the test shall 
be rejected and a new one made. 

Rejection by reason of failure to pass the shatter test shall not take 
place until at least two check tests have been made. 

Fluxes 

The object of a flux is to render fusible the ash from the fuel, sand 
and rust from the iron, and dirt of any sort, found in the cupola, into 
slag and to put it in condition for easy removal. 

Slag always forms to a greater or less extent where iron is melted, 
but unless a flux is present, it will not be sufficient in volume to give 
clean iron. Limestone and fluor spar are the most corrimon fluxes in 
use. There are many compounds furnished for the purpose, but a 
limestone containing 90 per cent or more carbonate of lime, or oyster 
shells, furnish as good fluxing material as can be procured. 

The following is copied from a paper by Mr. N. W. Shed, presented 
to the Cleveland meeting of the American Foundrymen's Association 
at June, 1906. 



430 Foundry Fuels 

"The value of fluxes in the cupola is not generally appreciated by 
foundrymen. Hundreds of cupolas are not slagged at all and the 
cinder dumps show an immense amount of iron actually wasted. Not 
only is iron lost by the large amount combined with the cinders, but the 
more or less variable cinder encloses small masses and shots of iron 
which cannot be separated. It is a fact that the cinder dumps of many 
foundries contain more iron than many workable deposits of iron ore, 
and if these accumulations could be obtained by the Geiman blast fur- 
naces they would be quickly utilized. 

Another value of fluxes is their cleansing action on the cupola. 
A weU slagged cupola has no hanging masses of iron and cinder which 
require laborious chipping out. The time and labor saved in conse- 
quence is an item that is well worth considering. In the running of 
heavy tonnage from a single cupola, fluxes are indispensable. It would 
be well nigh impossible to run large heats in the same cupolas without 
using a good flux. 

The value of fluxes being generally admitted, the question arises, 
what flux is best to use and how much? 

There are two available fluxes for the cupola. These are limestone 
and fluor spar. 

Fluor spar is much advertised as a flux and the promoters claim that 
it gives marvellous properties to the iron. The glowing advertisements 
have evidently deceived the U. S. Geological Survey, for the reports 
of the Survey speak of its great use and value in foundry practice. " 

The practical test of fluor spar, made by the writer showed it to be 
an inferior flux. It did not remove sulphur and the properties of the 
iron were not improved in the least by its use. There is no doubt of 
the value of fluor spar in certain branches of metallurgy, but the writer 
has failed to find a single supporter of its value in the foundry. 

Limestone is far cheaper than fluor spar and far better as a flux. 
It makes little difference what form the limestone has so long as it is 
pure. It may be marble, soft limestone, hard limestone, oyster shells, 
or mussel shells, but it must be good. A limestone containing over 
3 per cent sihca is poor stuff, and one containing any considerable 
amount of clay should be rejected. There should be at least 51 per cieht 
of lime present. The sulphur should be below i to 2 per cent. The 
phosphorus is unimportant. A magnesian limestone would do as well 
as an ordinary limestone for the cupola. 

The amount of limestone to be used is variable, depending: 

First: on the amount of silica in the coke ash. 

Second: on the amount of siUca or sand adhering to the pig or scrap. 

Third: on the amount of silica to be carried by the slag. 



Fluxes 431 

The amount of limestone required to flux the coke ash can be 
figured according to the ordinary method of calculating blast furnace 
charges. 

The amount of sand on the pig and scrap is so variable that it is 
difficult to know just the additional amount of limestone to add. 

The most practical and easily fusible slag has been found to be a 
monosilicate, which means having equal amoimts of silica and alkaline 
bases. Having these variables in mind, we find it a good rule to figure 
the hmestone on the weight of the coke, using 25 per cent hmestone. 

For example, if the charge of coke on the bed is 4000 pounds, we 
use 1000 pounds of limestone. If the next charge of coke is 1000 pounds, 
we would use 250 pounds of limestone. This amount of limestone will 
flux any ordinary coke ash with the average amount of sand on pig 
and scrap. If we know the amount of sand on the pig to be excessive 
we figure 30 per cent limestone on the weight of the coke. 

With a low coke ash, machine pig and clean scrap, the limestone 
may be reduced to 20 per cent and make a good cinder. Many foundry- 
men are afraid to use limestone, fearing some injury to the iron. This 
is a superstition for lime has no effect on the iron. 

There is usually a slight reduction in the amount of sulphur, but 
owing to the great amount of iron present, the iron absorbs a large 
amount of sulphur from the coke. 

If more than 30 per cent is required to make a good cinder and clear 
the cupola it is evident that either the coke is very high in ash, or else 
the limestone is high in silica. In the latter case a large amount of 
lime is used in fluxing its own silica. 

On account of the frequent variations in the stock, it is a good plan 
to have coke, limestone and cinder analyzed occasionally. 

The cinder usually tells about the condition of the furnace. A light 
brown indicates a small amount of iron and the iron unoxidized. A 
black cinder indicates a large amount of iron and some oxidation. A 
shiny metallic lustre shows an excess of oxide of iron due to over-blow- 
ing or lack of coke. Practically all the lime cinders from a cupola are 
glossy in appearance, while the cinders with no lime are usually dull 
and earthy. Occasionally a cinder is found full of bubbles, the color 
is usually black and shots of iron are found through the frothy slag. 
This is called foaming cinder, and is made when the last few charges 
are at the bottom of the cupola. This cinder often rises to the charging 
door and flows out over the floor. The iron cast at this time is hard 
and is low in manganese, silica and carbon. 

With foaming slag a dense smoke of reddish brown color pours out 
of the stack. 



432 



Foundry Fuels 



Analysis of the foaming slag shows the iron to be in an oxidized 
condition and in large amount. Sometimes the iron will run 30 per 
cent in frothy cinder, sometimes only 12 per cent. The oxidized cinder 
and the red smoke show that iron is being rapidly burned in the cupola, 
and the action going on is very much like the action in a Bessemer con- 
verter when it is tilted back a little and blown to gain heat by burning 
the iron. The cinder is oxidized and the red smoke is produced in the 
same way. In both cases the iron is burnt to oxide, which is quickly 
taken up by the slag. The oxide in the slag acts upon the carbon in 
the iron forming a large amount of carbonic oxide, which rises through 
the cinder blowing it to a frothy condition. 

There are two ways of avoiding this troublesome condition. If 
possible, reduce the blast. If the blast cannot be reduced, add more 
coke. The presence of a good body of coke will stop the burning of the 
iron, and frothing does not take place. In some cases the loss of sili- 
con is very serious, and to insure good castings it is necessary to add 
crushed silicon metal and ferro-manganese to the stream of iron as it 
runs from the spout. 

Analysis of cupola slags where no flux is used show from 14 to 28 per 
cent ferrous oxide. These slags contain 2 to 4 per cent of shot iron 
mingled with the cinder. This proves that some of the iron must be 
lost in order to flux the coke ash and sand. If we use limestone as a 
flux the amount of iron in the cinder is rarely over 3 per cent, showing 
that the lime fluxes the ash and sand leaving the iron for the ladle. 
And the question is simply whether we will use iron as a flux at ^18.00 
per ton or limestone at ^1.50 per ton. 

Another point in favor of the limestone is the clean cupola men- 
tioned in the first part of this paper. 

Following will be found an analysis of cupola cinder using lime." 



Comparison of Analyses of Slags, Made With and Without 
Lime 



Constituents 


Using 
lime 


Without 
lime 


CaO 


34.60 

4.10 

11.02 

48.20 

1.40 

.20 

99-52 


6.60 
21.76 
11.80 
58.44 

1.30 
.10 


FeO 


AI2O0 .. 


SiOs 


MnO 


S 


Total 


100.00 





Slags 433 

The following analyses are extracted from " The Foundry," Dec, 
1909- 

Analysis of Slag from a Cupola Melting Car Wheel Iron, in the South 

Per cent Per cent 

Silica 48 . 77 Oxide of iron 13.18 

Aluminum 10 . 90 Metallic iron 9 . 23 

Lime 13 • 79 Manganese . 4 . 84 

Magnesia 6.05 Sulphur 0.81 

Analysis of Slag from a Cupola Melting Gray Iron, No Fluor spar 
Being Used 

Per cent Per cent 

Silica 42 . 84 Magnesia 13 • 28 

Alumina Manganese 2 . 34 

Oxide of iron 21.32 Manganese oxide 3 . 01 

Lime 21.16 

Analysis of Slag from a Cupola Melting Gray Iron, Fluor spar 
Being Used 

Per cent Per cent 

Silica 39 • 50 Magnesia n . 05 

Alumina Manganese 2 . 24 

Oxide of iron 22.82 Manganese oxide 2.89 

Lime 24.50 

Analysis of Slag from a Cupola Melting Malleable Iron 

Per cent Per cent 

Silica. . . . : 41 • 72 Magnesia 15 .06 

Oxide of iron Manganese 3 . 20 

Alumina 22 . 24 Metallic iron S . 82 

Lime 17-84 Manganese oxide 4.12 

Analysis of Slag from a Cupola Melting Car Wheel Iron, in the North 

Per cent Per cent 

Silica 44.00 Magnesia 7.27 

Oxide of iron 13 • 16 Metallic iron 9.21 

Alumina 9.76 Manganese 5 . 70 

Lime iS-99 Sulphur 0.78 

Cupola Slag from a Western Foundry 

Per cent Per cent 

Silica 37 -16 Oxide of iron 13-73 

Alumina 9 . 16 Metallic iron 9 . 61 

Lime 8-98 Manganese oxide. ... 2 . 77 

Magnesia 8.44 Sulphur 0.36 



434 



Foundry Fuels 



Sufi&cient flux must be used to obtain a fluid slag to carry off the 
silica from the iron and ashes and to reduce the oxidation as much as 
possible. 

With low blast pressure the slag must be thin, to run off readily. 

When slag wool is freely produced, the indication is that the slagging 
is satisfactory. 

A good slag contains approximately 40 per cent of silica and from 28 
to 30 per cent lime. If the slag is thin, the metaUic iron will fall through 
it readily and an increase of lime tends to decrease the oxide of iron. 

Rusty scrap produces a dark-colored slag caused by the oxide of 
iron. 

A large body of slag is favorable to desulphurization, as the amount 
of sulphur which can be taken up by the slag is limited. At high temper- 
atures sulphur tends to combine with the slag and under these conditions 
it has not its greatest afi&nity for iron. 

Fire Brick and Fire Clay 
A good brick has a light yellow color, a coarse and open structure, 
uniform throughout. It should be burned to the limit of contractility. 
The clay from which it is made should contain as little iron, lime, potash 
and soda as possible. 



Analyses op Fire Clays Used por Making Fire Brick 

Clay loses its plasticity at a temperature above 100° C, and it cannot again 
be restored. 



Localities 


J 


CO 


C3 
g 

< 


"o 

4) C 

0" 


s 




1 


1 


Stourbridge, Eng. 


17.34 
12.74 
11.70 
5. 34 
5.4s 


45.25 
50.45 
49 -20 
59-95 
70.70 
55.62 
56.12 


28.77 
35.90 
27.80 
33.85 
21.70 
38.55 
37.48 


7.72 
1.50 

4.17 
4.43 


.47 . 
.13 
.40 
2.05 
.40 
.24 
.36 


20 
10 
55 
37 
24 
29 


• 95 
.99 




Mt. Savage, Md. 




Mineral Point, Ohio 




Port Washington, Ohio 




Springfield, Pa. 


24 


Springfield, Pa. 




.23 









Pure silicate of alumina melts at 1830° C. 

Fire bricks should stand continuous exposure to high temperatures 
of the furnace without decomposition or softening; should stand up 
under considerable pressure without distortion or fracture; should be 
unaffected by sudden and considerable variations of temperature; should 
not be affected by contact with heated fuel. 



Fire Sand 



435 



Fire brick should be regular in shape and uniform in character. The 
size of the ordinary straight fire brick is 9 by 4y2 by 2y2 inches, and the 
weight is 7 pounds. 

Cupola brick are usually 4 inches thick and 6 inches wide radially. 

Slabs and blocks are made in sizes up to 12 by 48 by 6 inches. 



Silica Brick 
Silica brick are used for resisting very high temperatures. They are 
composed mostly of silica in combination with alkaline matter. 
They are somewhat fragile and need careful handling. 

Analysis of Silica Brick 



Silica 


Alumina 


Ferric 
oxide 


Lime 


Magnesia 


Potash 


97.5 
90.0 


1-4 
3.0 


.55 
.80 


.15 
.20 


.10 
.10 




.6 



Canister 
Canister is made from an argillaceous sandstone, is a close-grained 
dark-colored rock containing no mica. There is present sufiicient clay 
to cause the particles to become adherent under ramming, after the rock 
has been ground. The rock is ground to a coarse powder and some- 
times if the binding properties are insufficient a little milk of lime is 
added during the grinding process. The composition of ganister will 
fall in the limits as given below. 



Constituents 


Per cent 


From 


To 


Silica 


87.00 
4.00 


95.00 

5.00 

1.50 

.75 

1. 00 


Alumina 


Ferric oxide 


Lime and Magnesia 


.25 


Alkalies 







Fire Sand 

An exceedingly refractory sand containing sometimes as much as 
97 per cent silica. It is used in the setting of silica brick and in making 
the hearths of furnaces. 

Pure silica melts at 1830° C. 



436 Foundry Fuels 

Magnesite 

Magnesite contains a small percentage of lime and ferrous silicates 
with serpentine. The ferrous silicates are separated out; thereupon 
calcining, magnesia is obtained. The calcined material is then mixed 
with from 15 to 30 per cent of the raw material, and from 10 to 15 per 
cent water, then moulded into briclis, dried and burned in the ordinary 
manner. 

Bauxite 

This is a hydrated aluminous ferric oxide, containing usually about 
60 per cent of alumina, i to 3 per cent of silica, 20 per cent ferrous oxide 
and from 15 to 20 per cent water. It is very refractory and, notwith- 
standing the large amount of ferrous oxide contained, is practically 
infusible. 

Calcined bauxite is mixed with from 6 to 8 per cent of clay, or other 
binding material and plumbago, then molded into bricks. 

When heated the plumbago reduces the iron of the bauxite, producing 
a most refractory substance. 

Such bricks are far more durable than the best fire bricks. They resist 
the action of the basic slags, as well as that of intense heat. 

They become extremely hard after exposure to continued heat. 



CHAPTER XIX 
THE CUPOLA 

The cupola is used in ordinary foundry practice in preference to the 
air furnace, not only on account of its simplicity, but because it melts 
more rapidly and economically. There are many forms manufactured. 
All of them are good, but it is doubtful if any furnishes better results 
than have been obtained from the ordinary old-fashioned cupola so 
commonly in use, such as is shown in the sketch below. 

For the advantages of the various styles offered for sale, the reader is 
referred to the manufacturers' catalogues. 

The cupola is essentially a vertical hollow cylinder, lined with refrac- 
tory material, having the top open and the bottom closed, with pro- 
vision for admission of the charges of fuel and iron part way up on the 
side, also for admission of air below the charges and for drawing off 
the melted metal at the bottom. 

The cupola is divided into five zoiies. 

First: The Crucible, extending from sand bottom to the tuyeres. 

Second: The Tuyere Zone, extending kom the crucible to melting 
zone. 

Third: The Melting Zone, reaching from the tuyere zone to a point 
about 20 inches above the tuyeres. 

Fourth: The Charging Zone, extending from melting zone to charging 
door. 

Fifth: Stack, from charging door to top of furnace. 

The Lining 

The lining is usually made of two thicknesses of arch brick placed 
on end with the flat sides in radial planes. Several standard rectangular 
brick are placed in each ring or course to facihtate the removal of the 
rings when necessary. Angle iron rings are riveted to the shell at 
intervals of about six feet, to support the upper sections, when a lower 
one is removed for repairs. 

The outer lining is kept about Yi inch away from the shell to pro- 
vide for expansion, and the interval is filled in loosely with sand and 
broken brick. 

437 



438 



The Cupola 



The distance from the sand bottom to the charging door should be 
about 31/i to 4 times the inside diameter of the lining. For cupolas 




Fig. 123. 

under 48 inches, one door is, sufficient; for larger sizes two are more 
convenient. The doors may be hung on hinges or slide on a circular 
track above the openings. It is not necessary that they should be lined. 



Tuyeres 



439 



At the level of the charging door the lining should be covered with a 
cast-iron ring to protect it during the charging. 

The bricks are laid with very close joints in mortar composed of 
fire clay and sand. The interior lining is daubed with a mixture of one- 
half fire clay and three-fourths sharp sand for a thickness of three- 
fourths inch. Any joints are well filled. A handful of salt to a pail of 
daubing will cause the interior of the shell to be glazed over and will 
reduce the amount of chipping required. Washing the daubing with 
strong brine and fire clay serves the same purpose. 

Tuyeres 

The tuyeres may be circular or rectangular in section with the bottoms 
inclining slightly toward the interior of the shell so that the drippings 
may not run into the wind box. Castings for tuyeres should not be 
over ^i inch thick. 

The area of the tuyeres is made from lo to 25 per cent that of the 
inside fining at the tuyeres; 20 per cent gives good results. As a matter 
of fact the tuyeres cannot be made too large. A continuous tuyere 
having an opening about 2 inches in height and extending all around the 
lining is frequently used. 

An excellent plan is to have an air chamber 
all around the outer lining and inside of the 
shell in the vicinity of the tuyeres; at the 
level of the bottom of the tuyeres place a 
cast-iron ring, in sections, on top of the 
double lining. On this, at intervals of from 
7 to 10 inches, so as to divide the circum- 
ference of the interior of the lining into equal 
parts, place hollow iron blocks 2 inches wide, 
3 inches high and 7 inches long. On top of the 
blocks place another segmental ring, which ^^' ^^^" 

shoiild be kept 3 or more inches away from the interior of the shell. 
Upon this ring the upper courses of the lining are built. This forms 
a nearly continuous tuyere, broken only by the iron blocks. 

This construction involves a contraction of the fining at the tuyeres 
of about 8 inches. The bottom of the tuyeres should be from 10 to 
20 inches above the sand bottom, depending upon the quantity of 
melted iron to be collected before tapping. Where the iron is allowed 
to run continuously from the spout, as in stove and other foundries 
doing fight work, the tuyeres may be even lower than 10 inches. 

Frequently an additional row of tuyeres, having about one-eighth of the 
main row in area, is placed just below the melting zone. These upper 




440 The Cupola 

tuyeres should be arranged so that the admission of air through them 
may be regulated. The object is to supply the necessary air to convert 
whatever carbonic oxide is formed in. the tuyere zone into carbonic acid 
at the melting zone. The heat developed at these upper tuyeres is such 
that the Uning near them is often badly cut, therefore, care must be 
exercised as to the admission of air at this point. 

A row of adjustable tuyeres about lo inches above the melting zone 
is most effective in producing the combustion vvithin the charges of 
carbonic oxide, forced above that zone, effecting thereby not only a 
saving of fuel, but the suppression of flame at the charging doors. The 
admission of air above the melting zone must be carefully regulated so 
that only enough will enter to burn the carbonic oxide. 

The "Castings" for September, 1908, illustrates a cupola designed 
by Mr. J. C. Knoeppel, which presents an admirable arrangement of 
tuyeres and provides for the object above outlined. 

Two or more of the lower tuyeres, should have slight depressions 
in the bottoms, to permit the slag or iron, should either reach that 
level, to run out upon sheet lead plates placed in the wind box in 
the line of these depressions. By the melting of these plates, and 
the discharge through the resulting holes, warning is given to the 
cupola tender, and the accumulation of slag or iron in the wind box 
avoided. 

Unless the blast is much higher than good management permits, it 
will not penetrate the fuel in the cupola for more than 30 inches radially, 
Therefore, where the inside diameter of the cupola is over 6c inches, 
it should be contracted at the tuyeres to 60 inches or less diameter; 
or in place of this a center blast may be used. Large cupolas are fre- 
quently made oval in section with the same object in view. 

In the wind box directly opposite each tuyere there should be a small 
door 5 inches in diameter, fastened with a thumb screw, for access to 
the tuyeres, to remove any stoppages in front of them; each door should 
be provided with a peek hole i>i inches in diameter covered with mica. 

The Breast 

The breast is made by taking a mixture of one-half fire clay and one- 
half molding sand, thoroughly mixed and just moist enough to be 
kneaded. A quantity of this is placed around a bar 13.4 inches in diam- 
eter and made into cylindrical shape, 4 or 5 inches in diameter and about 
6 inches long. This is placed in the opening for the breast, and the bar, 
while held in a nearly horizontal position, forced down until its bottom 
is on a line with the sand bottom, and % inch above the upper side of 



Sand Bottom 441 

lining to trough. The inner end of the clay cylinder should be flush 
with the inside of the cupola hning. 

Ram hard around this cylinder with molding sand and fill opening 
for breast completely. Care must be taken that this clay cyhnder is 
well secured in place. Remove the forming bar and enlarge the hole 
toward inside of cupola, leaving only about 3 inches in length of the 
original diameter from the front. 

The slag hole is made up in same way, but should be only one and a 
half inches long. A core about 2H inches in diameter may be inserted 
for the slag hole, and this dug out, when tapping for slag, until opening 
is sufficiently large, say about i inch diameter. 

It sometimes happens that the breast gives way during the heat. 
In such an event, the blast is shut off and the cupola drained of iron and 
slag. The defective part of the breast is removed, and replaced with 
stopping clay, which is hammered with the side of a bar, well against 
the surrounding portion of the breast. The remaining hole is then filled 
with clay, carefully packed so as not to be driven to the interior of the 
cupola. Through this clay a tap hole is made by gently inserting the 
tapping bar and enlarging the hole after the ball of clay has been pene- 
trated. In from fifteen to twenty minutes the clay will have been 
baked hard. The blast can then be turned on and melting resumed. 
This operation must be conducted with great care, as the operator is 
in danger of being severely burned. 

Swab the lining from the bottom to 2 feet above the tuyeres with 
clay wash and salt, and black wash the tapping hole formed as above 
described. 

Sand Bottom 

The sand bottom is made from gangway sand passed through a No. 4 
riddle. This bottom should be about 8 inches thick. It must be well 
rammed, especially next to the lining, where it should join with a liberal 
fillet. It must not be too wet. Care must be taken not to ram the 
bottom so hard that the iron will not lie on it quietly. The bottom 
should slope in all directions towards the tapping hole, the slope being 
one inch in four feet, and it should reach the tapping hole exactly on a 
level with its lower surface. 

Black wash the bottom, build a light wood fire and dry out the lining 
thoroughly. The bottom doors should have a dozen or more %-inch 
holes drilled through them to allow any moisture in the bottom to 
escape. The doors are held in place by an iron post under the center, 
which can readily be knocked out to drop the bottom. The breast 
should be made up before the bottom. 



442 The Cupola 

Zones of Cupola 

The crucible zone extends from the sand bottom to the tuyeres. 
The object of this zone is to hold the melted iron and slag. If the tap 
hole is kept open continuously, this zone may not be over 4 to 6 inches 
in depth from sand bottom to bottom of tuyeres. If it is to hold a 
large quantity of melted iron, the tuyeres must be correspondingly 
high. Metal can be melted at a higher temperature with low tuyeres, 
(collecting it in a ladle), than by holding it in 'the cupola. 

Tuyere Zone 

This is where the blast enters in contact with the fuel. Here com- 
bustion begins. This zone is confined to the area of the tuyeres. The 
combined area of the tuyeres should be about one-fifth that of a section of 
the cupola at this point, and should also largely exceed that of the outlet 
of the blower. It is important to keep the tuyeres as low as the condi- 
tions of the foundry, as to amount of melted iron to be collected at one 
tap, will permit. With low tuyeres the iron is hotter, there is less oxida- 
tion and the fuel required on the bed is less. 

Melting Zone 

The melting zone is the space immediately above the tuyeres. It 
extends upward from 20 to 30 inches, depending upon the pressure and 
volume of the blast, increasing in height with increased pressure. No 
iron is melted above or below it. The melting occurs through the upper 
4 to 6 inches of that zone. 

Charging Zone 

This zone is that part containing the charges of iron and coke, and 
extends from the melting zone to charging door. 

The stack is the continuation of the cupola from charging door through 
the roof. Contracting the stack above the charging door has no influ- 
ence upon the efficiency of the cupola. 

The spouts should be lined with fire brick. Above the fire brick 
bottom at center of trough, there should be iVi inches of moulding 
sand. From the center the sand should slope rapidly each way to 
sides. The sand lining of trough at' center should be % inch below 
the tap hole. After lining, trough should be black washed and dried. 
Stopping material is made of one-half fire clay and one-half moulding 
sand. 

It is the common practice to leave the top hole open until iron begins 



Chemical Reactions in Cup)ola 443 

to run freely, in order to prevent freezing at the hole. This causes 
the oxidizing of considerable metal, and is unnecessary. The following 
method may be pursued. Just before the blast goes on, close up the 
inner end of the tap hole with a ball of greasy waste, then ram the 
remainder of the hole full of moulding sand. This is easily removed 
with the tapping bar, and does away with all the annoyance of escaping 
blast and sparks. 

Chemical Reactions in the Ordinary Cupola with 
Single Row of Tuyeres 

When the air blast comes in contact with the burning coke, its oxygen 
unites with the carbon of the coke to form carbonic acid (CO2), as the 
result of complete combustion. As the temperature above the tuyeres 
increases to that necessary for melting iron, part of the CO2 seizes upon 
the incandescent coke, takes up another equivalent of carbon and is 
converted into carbonic oxide (CO). If the supply of air is in excess 
of that required, the CO, being combustible gas, takes up another 
equivalent of oxygen and is burned to CO2. 

Again some of the CO2, parting with an equivalent of oxygen to the 
iron for such oxidation as occurs, or by the acquisition of another equiva- 
lent of carbon from the coke; or by both, is reconverted into CO. These 
reactions take place at or near the melting zone. 

After passing that zone, no more air is supplied, and the products of 
combustion, consisting of CO and CO2 pass up the stack without further 
change until reaching the charging door. Here air is admitted, the 
CO is supplied with oxygen and is burned to CO2. 

If the air supplied at the tuyeres is insufi&cient for complete combus- 
tion, the evolution of CO is increased and the efficiency of the furnace 
reduced. On the other hand, an excessive supply of air is objectionable, 
as a reducing flame (that from CO) is desirable to prevent oxidation 
of the metal. 

For the complete combustion of one pound of carbon, there is required 
12 pounds, or about 150 cubic feet of air, developing 14,500 B.t.u.; but 
the combustion of one pound of carbon to CO requires only one-half the 
air, and the resulting heat is 4500 B.t.u.; hence for whatever portion of 
the fuel is burned to CO, there is a loss of over two-thirds its heat- 
producing value. 

For the purpose of saving this waste heat, an upper row of tuyeres, 
just below the melting zone, is employed; and to utilize the heat which 
escapes above the melting zone, tuyeres have been introduced with 
good results, at from 5 to 10 inches above that zone. By the use of 



444 



The Cupola 



the latter tuyeres the heat developed is absorbed by the charges in the 
stack, and the flames at charging door are suppressed. Where such 
tuyeres are used, they must be provided with means for easily regulating 
the admission of air. 

The following table taken from West's Moulders' Text Book gives 
the quantity of air required for the combustion of one pound each of 
coke and coal. 



Combustibles, 
I pound weight 


Weight of oxy- 
gen consumed 
per pound of 
combustible, 
pounds 


Quantity of air con- 
sumed per pound 
of combustible 


Total heat of ' 
combustion 
of I pound of 


Pounds 


Cubic feet 
at 62° F. 


combustible, 
units of heat 


Coke, desiccated 

Coal, average 


2.51 
2.46 


10.9 
10.7 


143 
141 


13,550 
14,133 







By reason of the contact of the molten iron with the fuel, changes in- 
atmospheric conditions, the amount of air used, and other conditions, 
the same mixtiu-e may produce different kinds of castings at different 
times; and there may also be variations in the same heat. 



Chemical Reactions in the Cupola 

The complete combustion of one pound of carbon to CO2 requires: 
2.66 pounds of oxygen 
or 12.05 pounds of air 

and develops 14,500 B.t.u. 

The burning of one pound of carbon to CO requires: 
1.33 pounds of oxygen 
or 6.00 pounds of air 

and develops 4500 B.t.u, 

Therefore one pound of coke, having 86 per cent fixed carbon requires 
for complete combustion 

2.66 X 0.86 = 2.29 pounds oxygen 
or 12.00 X 0.86 = 10.32 pounds air 

and develops 14,500 X 0.86 = 12,470 B.t.u. 

The 10.32 pounds of air less 2.29 pounds oxygen leave 8.03 nitro- 
gen. 



Wind Box 445 

Taking the specific heat of oxygen at 0.218, carbon at 0.217, nitrogen 
at 0.244. The temperature resulting from the complete combustion of 
one pound of coke to CO2 is 

12,470 ^ o p 

0.217 X 0.86 + 0.218 X 2.28 + 0.244 X 8.03 ^' 
That resulting from the combustion of one pound of coke to CO is 

3870 . ^ O p 

0.217 X 0.86 + 0.218 X 1.15 + 0.244 X 4.015 

Hence for every pound of coke burned to CO, instead of CO2, there is 
a loss of 8600 B.t.u., and a reduction of the resulting temperature of 
1983° F. Taking the specific heat of cast iron at the average of temper- 
atures between 2120° and 2650° F. as 0.169, and the latent heat of fusion 
as 88 B.t.u., and assuming the temperature of the escaping gases at 
1330°, then the heat wasted is (i330°-7o°) X (0.217 X o-86 + 0.218 
X 2.28 + 0.244 X 8.03) equals 3330 B.t.u.; . and the heat available for 
melting iron is 12,470 — 3330 = 9140 B.t.u. for each pound of coke 
having 86 per cent fixed carbon. 

For I pound of iron melted at 2650° F. (or 2580° F. above atmosphere) 
the number of heat units required is 2580 X 0.17 = 439 to which must 
be added the latent heat of fusion giving 439 + 88 = 527 B.t.u. 

Therefore, - — = 17.^4 pounds of iron, which should be melted by 
' 527 ' ""^ ^ • 

one pound of coke, if all the carbon was converted into CO2 and the gases 
escaped at 1330° F.; also neglecting the heat lost in the slag and by 
radiation. 

Wind Box 

The area of cross section of the wind box should be three or four times 
that of the combined area of the tuyeres, in order that there may be 
sufficient air reservoir to permit a steady pressiu"e. There should be 
two or more doors in the box for ready access in cleaning out when 
necessary; and also for admission of air when the wood fire is started. 
As before stated, there should be small doors opposite each tuyere. 

The blast pipe ought, if the situation will permit, to enter the box on 
a tangent, and box should be continuous. If it is necessary to divide 
it into two boxes, on account of the tapping or slag holes, there must, 
then, of course, be a blast pipe for each box and they should enter the 
boxes vertically. 

The bottom of the box should be provided with at least two small 
openings opposite the alarm tuyeres, which are covered with sheet lead. 
These should be so placed that slag or iron running through them will 
be at once seen by the tapper. 



446 



The Cupola 



The manufacturing of cupolas for the trade has become an important 
industry, and although the designs of the various makers differ largely 
in details, the essential features in all are the same. 

Perhaps the names best known to the foundry industry are: CoUiau, 
Calumet, Newten, Whiting. 

All of these give good results. For special information reference 
should be made to the manufacturers' catalogues. 

The melting capacities based on 30,000 cubic feet of air per ton of 
iron are given in the following table. 

Builders' Rating 



Diameter 

inside of 

lining, 

inches 




Colliau 


Calumet 


Newten 


24 
30 
36 
42 
48 
54 
60 
66 
72 
78 
84 


Melting capacity, ^ 
tons per hour 


I- 1K2 
3- 4 
4-6 
6- 8 
8-10 

lO-II 

12-14 

15-16 

17-20 

. 25-27 


1- 2 

2- 3 
4- 5 
6-7 
8-9 

lo-ii 

12-14 . 

15-17 

18-20 

21-24 

24-27 


IH- 2l/^ 

3-5 
4.-6 

8 -9 

9 -II 

11 -12 

12 -14 
14 -18 
18 -20 
20 -24 







A wind gauge should be attached to the wind box at a convenient place. The 
charging platform should not be more than 24 inches below the bottom of charging 
door for sizes up to the 48 inch; for the larger sizes not over 6 to 8 inches. 

The Blast 

The air for the blast is supplied by centrifugal blowers of the Sturte- 
vant tj^e, or by Positive Pressure Blowers of the Root type. Both are 
efficient, and it does not appear that either has any special advantage 
not possessed by the other. 

For successful melting a large volume of air at low pressure is required. 
From 8 to 10 ounces pressure will usually be found sufficient; in no case 
should it be allowed to exceed 14 ounces. 

As a rule 30,000 cubic feet of air per ton of iron are allowed. This is 
somewhat too small, especially if the air contains much moisture; 
35,000 cubic feet per ton is better practice. 

With blast at low pressure and with high temperature in the furnace, 
iron may gain in carbon during the process of melting. The reverse 
may occur, however, under contrary conditions. Oxidation increases 
with the intensity of the blast. 



The Blast 



447 



The castings produced by low blast pressure are softer and stronger, 
the loss by oxidation is less, there is less slag, less expenditure of power 
and less injury to the lining of the cupola. 

Coke requires less pressure and more volume of air, as well as greater 
tuyere area than coal. 

Low pressure, large volume, large tuyere area and good fluxing tend to 
prevent choking at the tuyeres. However, too much air must be avoided 
as it reduces the temperature of the furnace and may produce dull iron. 

The main blast pipe should be as short, and the tuyeres as few as 
possible. Its diameter should be greater than the outlet of the blower. 
For each turn allow three feet in length of pipe. The minimum radius 
of the turn should not be less than the diameter of the pipe. It should 
be provided with a wind gate, and, where a pressure blower is used, an 
escape valve, both under control of the melter. The wind gate should 
be kept closed until after the blower is started to prevent gas from 
collecting in the blast pipe. For the same reason, the blower should, if 
possible, be located lower than the wind box. 

At the commencement, the blast should be low, and gradually in- 
creased to the maximum as the heat progresses, then dropped toward 
its close. 

The friction of air in pipes varies inversely as their diameters, directly 
as the squares of the velocities, and as the lengths. The table below 
shows the loss in pressure and the loss in horse power by friction of air 
in pipes loo feet long; corresponding losses for other lengths can readily 
be calculated therefrom. 



Loss IN Pressure in Ounces and Horse Power in Friction 
OF Air in Pipes ioo Feet Long 



Diam- 
eter of 


Tons of 


Cubic 


Velocity 


Diam- 


Diam- 


T,o,ss of 


Horse 


cupola 


iron 


feet of 


of air 
in feet 


eter of 
blast 


eter of 


pressure 


power 


inside of 


melted 


air per 


outlet of 


in ounces 


lost in 


lining, 
inches 


per hour 


minute 


per 
minute 


pipe, 
inches 


blower 


per square 
inch 


friction 


24 


1.5 


875 


1600 


10 


8 


.313 


.099 


30 


3.0 


i,7So 


2200 


12 


9 


.448 




211 


36 


4.5 


2,600 


2400 


14 


II 


.457 




320 


42 


6.0 


3.500 


2500 


16 


12 


.434 




40s 


48 


8.0 


4,700 


2600 


18 


14 


.417 




523 


54 


10. 


5,800 


2700 


20 


15 


.406 




653 


60 


12.5 


7,300 


2300 


22 


18 


.246 




485 


66 


15.0 


8,750 


2400 


24 


20 


.246 




594 


72 


18.0 


10,500 


2500 


26 


22 


.231 




582 


78 


22.0 


12,800 


2500 


28 


23 


.202 




507 


84 


25.0 


14,560 


2600 


30 


24 


.190 




498 



Computed from catalogue of B. P. Sturtevant & Co., and from Foundry Data 
Sheet No. 5. 



448 



The Cupola 



The following tables give the capacities of centrifugal and pressure 
blowers. As these are based on 36,000 cubic feet of air per ton of iron, 
the selection of sizes somewhat larger than those given in the tables is 
desirable, as the allowance of air is too small. 



The Sturtevant Steel Pressure Blower Applied to Cupolas 



No. of 
blower 


Diam- 
eter of 
inside of 
cupola 
lining 


Melting 
capacity 
per hour 

in 
pounds 


No. of 

square 

inches of 

blast 


Cubic 
feet of 
air per 
minute 


Speed 


Pressure 
in ounces 
of blast 


Horse 

power 

required 


I 


22 


1,200 


4.0 


324 


413s 


5 


0.5 


2 


26 


1,900 


5.7 


507 


3756 


6 


i.o 


3 


30 


2,880 


8.0 


768 


3250 


7 


1.8 


4 


35 


4,130 


10.7 


1 102 


3100 


8 


3.0 


5 


40 


6,178 


14.2 


1646 


2900 


19 


5.5 


6 


46 


8,900 


18.7 


2375 


2820 


12 


9-7 


7 


S3 


12,500 


24.3 


3353 


2600 


14 


16.0 


8 


60 


16,560 


32 


4416 


2270 


14 


22.0 


9 


72 


23,800 


43.0 


6364 


2100 


16 


35. 


10 


84 


33,300 


60.0 


8880 


1815 


16 


48.0 



The Sturtevant Steel Pressure Blower Applied To Cupolas 

(Power saved by reducing the speed and pressure of blast.) 



Speed 


Pressure, 


Horse 


Speed 


Pressure, 


Horse 


ounces 


power 


ounces 


power 


3445 


5 


.8 


3100 


4 


.6 


3000 


6 


1.5 


2750 


5 


I.I 


2900 


7 


2.5 


2700 


6 


2.0 


2560 


8 


4.0 


2390 


7 


3.3 


2550 


10 


7-4 


2260 


8 


5.3 


2380 


12 


12.7 


2150 


10 


9.4 


2100 


12 


16.7 


1900 


10 


12.7 


i960 


14 


28.4 


1800 


12 


22.5 


1700 


14 


39-6 


1566 


12 


31.7 















Kent, page S19. 



Pressure and Rotary Blowers 



449 



Buffalo Steel Pressure Blowers Speeds and Capacities as 
Applied to Cupolas 



Square 
inches 
in blast 





Diam- 
eter 




Speed, 


Melting 


Cubic 
feet of 


No. of 
blower 


inside of 
cupola, 
inches 


in 
ounces 


No. of 

revs. 

per min. 


capacity, 
pounds 
per hour 


air 
reqmred 
per min. 


4 


20 


8 


4793 


1,545 


412 


5 


25 


8 


391 1 


2,321 


619 


6 


3o 


8 


3456 


3,093 


825 


7 


35 


8 


3092 


4,218 


1 125 


8 


40 


8 


2702 


5.425 


1444 


9 


45 


10 


2617 


7,818 


2085 


ID 


55 


10 


2139 


11,29s 


3012 


II 


73 


12 


1639 


21,978 


5861 


12 


88 


12 


1639 


32,395 


8626 



Horse 

power 

required 



i.o 
1.2 

2.0s 
3-1 
3.9 
7.1 
10.2 
23.9 
36.2 





Speed, 


Melting 


Cubic feet 




Pressure in 


no. of revs. 


capacity in 


of air re- 


Horse power 


ounces 


per mm. 


pounds per 
hour 


quired per 
minute 


required 


9 


5095 


1,647 


438 


1.3 


10 


4509 


2,600 


694 


2.2 


10 


3974 


3,671 


926 


3.1 


10 


3476 


4,777 


1274 


4.2s 


10 


3034 


6,082 


1622 


5.52 


12 


2916 


8,598 


2293 


936 


12 


2353 


12,378 


3301 


12.0 


14 


1777 


23,838 


6357 


30.3 


14 


1777 


35,190 


6384 


43.7 



Kent, page 950. 

The Root Positive Rotary Blowers 



Size 

number 


Cubic feet 
per revo- 
lution 


Revolutions 

per minute for 

cupola melting 

iron 


Size of cupola, 

inches inside 

lining 


Will melt iron 
per hour, tons 


Horse 

power 
required 


2 
3 

4 
S 
6 

7 


5 
8 
13 
23 

42 
65 


275-325 
200-300 
185-275 
170-250 
150-200 
137-175 


24-30 
30-36 
36-42 
42-50 
50-60 
72 or %5 


2l/^-3 

3-4^^ 
42/^-7 
8-12 
I2l/i-l6% 

17^-22% 


8 

17% 

27 

40 



Kent, page 526 



450 



The Cupola 



Diameter of Blast Pipes for Pressure Blowers for Cupolas 

B. F. Sturtevant ^ Co. 
The following table has been constructed on this basis, namely, allow- 
ing a loss of pressure of one-half ounce in the process of transmission 
through any length of pipe of any size as a standard; the increased fric- 
tion due to lengthening the pipe has been compensated for by an 
enlargement of the pipe, sufi&cient to keep the ioss still at y? ounce. 

The Blast 



Blower No. i 


Blower No. 6 


Cubic 
feet of 


Lengths of blast pipe in feet 


Cubic 

feet of 

air 


Lengths of blast pipe in feet 


air 






















trans- 


50 


100 


ISO 


200 


300 


trans- 


50 


100 


150 


200 


300 


initted 












mitted 

per 
minute 












per 
minute 


Diameter in inches 


Diameter in inches 


360 


5% 


6H 


6% 


71/4 


7% 


1,872 


10^^ 


I2H 


I31/4 


13% 


IS 


515 


63^ 


7\i 


7% 


-8H 


8/8 


2.679 


12H 


14 


15% 


16 


I7H 


635 


63/4 


7% 


m 


9 


9% 


3,302 


131/4 


15/8 


16/2 


iiYi 


18% 


740 


7H 


m 


9 


91/2 


loH 


3.848 


14!/^ 


16H 


I71/2 


18}.^ 


20% 


Blower No. 2 


Blower No. 7 


504 


614 


1% 


1% 


8I/4 


8/8 


2.592 


12 


133/4 


IS 


15% 


17% 


721 


714 


Wi 


9 


9K2 


iQi/i 


3,708 


13% 


15% 


17H 


I8H 


I9H 


889 


7% 


9 


934 


10^^ 


II 


4,572 


15H 


n% 


18% 


19% 


2I5% 


1036 


8^8 


9>i 


io% 


II 


II3/4 


5,238 


16 


18 H 


20 


211/4 


23 


Blower No. 3 


Blower No. 8 


720 


7^- 


m 


9 


m 


loM 


3,312 


13H 


15% 


16/2 


17!/^ 


18% 


1030 


%% 


q\i 


I03/8 


II 


Il2/ 


4,738 


15H 


17% 


I9i'i 


20% 


21% 


1270 


Q^ 


1034 


iiH 


11% 


123/4 


5,842 


16^^ 


19^/^ 


203/4 


22 


23% 


1480 


9% 


II 


12 


125,^ 


I3H 


6.808 


17^/^ 


20/4 


22% 


2m 


2S% 


Blower No. 4 


Blower No. 9 


1008 


m 


m 


loH 


I07/^ 


XT% 


4,320 


uH 


17 


18% 


19% 


21% 


1442 


9H 


loH 


11% 


12/2 


13% 


6.180 


17 


19}^ 


21/4 


22l/i 


2A% 


1778 


I034 


iiVs 


12% 


13^/^ 


uH 


7.620 


l83/i 


21% 


23% 


24% 


26% 


2072 


II 


125/8 


133/4 


14!/^ 


151/2 


8,880 


19^/2 


22/2 


24i^ 


26 


28% 


Blower No. 5 


Blower No. 10 


1440 


qH 


10% 


iili 


12H 


I33/i 


5,760 


im 


19 


20% 


21% 


23% 


2060 


II 


125^ 


1334 


I4i/i 


iSi/i 


8,240 


1^% 


21% 


233/4 


25% 


27H 


2540 


11% 


iM 


14% 


155/^ 


16% 


10.160 


205/i 


233/4 


25% 


21% 


29H 


2960 


12% 


I4H 


15% 


l65/^ 


18 


11,840 


22H 


2554 


27^ 


29% 


31H 



Kent, page 520. 



Dimensions, Etc., of Cupolas 



451 



The quantities of air in the left-hand column of each division indicate 
the capacity of the given blower when working under pressures of 4, 
8, 12 and 16 ounces. Thus a No, 6 blower will force 2678 cubic feet of 
air at 8 ounces pressure through 50 feet of 121-4-inch pipe with a loss of 
\i ounce pressure. If it is desired to force the air 300 feet without an 
increased loss by friction, the pipe must be enlarged to 17H inches 
diameter. 

The table below gives the important dimensions, distribution of 
charges and melting capacities of cupolas from 24 inches to 84 inches 
diameter inside of lining. The table is based upon the consumption 
of 3 5, 000 cubic feet of air per ton of iron and represents the best aver- 
age practice. 

Higher fuel ratios are frequently realized and the foundrymen must 
vary the fuel and air supply as the conditions indicate. It is imwise, 
however, to strive for high fuel ratio at the risk of a dull heat. The 
loss on castings from one melt may far outweigh the saving on coke, 
as between the ratios of 10 to^i and 9 to i, for many heats. Coke is 
one of the cheapest articles about the foundry; while hot, clean iron is 
an item of the highest importance. 

In general the cupola should furnish 20 pounds of melted iron per 
minute per square foot of area of the melting zone. 



Dimensions, Etc., of Cupolas 







Height 














Diameter 

of cupola 

inside of 

lining, 

inches 


Height 
from bot- 
tom-plate 
to charg- 
ing door, 
feet 


from 

sand bot- 
tom to 

underside 
of tu- 
yeres, 
inches 


Area of 
tuyeres, 
sq. in. 


Pounds 
of coke 
on bed, 
Jpounds 


First 
charge 
of iron, 
pounds 


Suc- 
ceeding 
charges 
of coke, 
pounds 


Suc- 
ceeding 
charges 
of iron, 
pounds 


Pres- 
sure of 

blast, 
ounces 


24 


9.0 


8-10 


90 


225 


320 


40 


320 


5- 7 


30 


10. 


8-10 


142 


370 


560 


62 


560 


6-8 


36 


10.6 


8-12 


204 


460 


850 


85 


850 


6- 8 


42 


10.6 


10-12 


277 


530 


1200 


no 


1200 


6- 8 


48 


12.0 


10-12 


362 


820 , 


1500 


140 


1500 


8-10 


54 


13.0 


10-15 


458 


1 100 


1900 


180 


1900 


8-10 


60 


15.0 


10-18 


S65 


1400 


2500 


225 


2500 


10-12 


66 


16.0 


10-18 


684 


1900 


3000 


275 


3000 


10-12 


72 


18.0 


IQ-20 


814 


2400 


4000 


320 


4000 


12-14 


78 


19.0 


10-20 


955 


3000 


5000 


400 


5000 


12-14 


84 


19.0 


ic-22 


1 108 


3600 


6000 


500 


6000 


14-16 



452 The Cupola 

Dimensions, Etc., oe Cupolas. — (Continued) 



Volume 


Diameter 
of blast 


Size of 
Root 


Num- 
ber of 


Horse 


Size of 

Sturte- 

vant 


Num- 
ber of 
revolu- 


Horse 
power 


Melting 
capac- 


of air per 


pipe not 


blower 


revolu- 


power 


blower 


tions 


re- 


ity per 


minute, 
cu. ft. 


over 100 

feet long, 

inches 


required, 
no. 


tions per 

minute, 

revs. 


required 
H.P. 


re- 
quired, 
no. 


per 

minute, 

revs. 


quired, 
H.P. 


hour, 
pounds 


875 


10 


I 


300 


2 


3 


3500 


2 


3,000 


1. 750 


12 


2 


300 


5 


5 


2900 


5-5 


6,000 


2,600 


14 


4 


175 


8 


6 


2800 


10 


9,000 


3.500 


16 


4 


230 


12 


7 


2600 


15 


12,000 


4.700 


18 


5 


200 


20 


8 


2300 


22 


16,000 


5.800 


20 


5i/i 


190 


25 


8 


2500 


25 


20,000 


7,300 


22 


6 


180 


33 


9 


2200 


35 


25,000 


8,700 


24 


6H 


170 


45 


10 


1800 


45 


30,000 


10,500 


26 


7 


150 


55 


10 


2000 


55 


36,000 


12,800 


28 


7'A 


150 


70 


2-8 


2500 


60 


44,000 


14,500 


30 


7H 


170 


80 


2-9 


2200 


70 


50,000 



Charging and Melting 

In preparing the cupola for melting, a bed of shavings is spread evenly- 
over the bottom; on this a layer of kindling wood; then enough cord 
wood cut in short lengths to come well above the tuyeres. The doors 
in the wind box or, two or more of those covering the tuyeres, should be 
left open to admit air to the fire. The wood should be covered with coke 
for a depth of from 12 to 15 inches. Where wood is scarce or expensive, 
the coke may be lighted directly with a kerosene oil blow torch. To use 
the torch place two strips of boards 3" X i" on edge from the tap 
hole to center of cupola. Then place other strips of same size crosswise 
of the bottom forming a shallow trough about 6 inches wide in the shape 
of a T. Large pieces of coke are placed over the trough to form a 
cover, and on top of this coke is spread uniformly for a depth of about 
15 inches. The torch is then applied at the tap hole. 

After the fire is lighted and the top of the coke bed becomes red, 
enough coke is added to bring the top of the bed 20 inches above the 
tuyeres when the wood has burned out. 

The necessary amount of coke for bottom is determined by gauging 
from the charging door. The proper depth of bed is a matter of great 
importance. Too much is as bad as too little. With too much coke, 
the melting will be slow and dull; with too little the iron after commence- 
ment of heat becomes dull, the cupola is bunged up and the bottom 
may have to be dropped. 



The Charging Floor 453 

There should be sufficient coke to locate the top of the melting zone 
about 20 inches above the tuyeres, and the subsequent charges of coke 
should be just enough to maintain this position. 

With proper depth of bed, the molten iron will appear at the spout in 
from 8 to 10 minutes after the commencement of the blast. The first 
and subsequent charges of iron should be of the same weight, and these 
should be small. 

The amount of coke between each charge of the iron and the preceding 
one should be 10 per cent of the iron. In many foundries the coke 
between the charges is made less than this, but 10 per cent is good 
practice. It is not the best policy to run the risk of making a poor heat 
by cutting down the coke. The charges should be continued as indi- 
cated until the cupola is filled to the charging door. 

In charging care must be taken to distribute both iron and coke uni- 
formly. 

The pig iron (broken) should be charged first, beginning at the lining 
and proceeding toward the center, pigs should be placed sidewise to the 
lining. Next comes the scrap; if there are large pieces, they should be 
placed in the center of the cupola with the pig surrounding them. 

The iron must be kept well around the lining and care exercised to 
avoid cavities. If the scrap is fine, it must not be charged so closely as 
to impede the blast. After the iron comes the coke, which must be 
evenly distributed throughout. After the second or third charge, lime- 
stone, broken into pieces about i}^ cube, is added. From 25 to 40 
pounds of limestone per ton of iron is used according to the character 
of pig and scrap as to sand and rust, and to that of coke as to ash. 

The top of the bed should not be permitted to drop more than 6 or 
8 inches during the heat. This determines the weight of iron for each 
charge as well as that of the coke, the latter having a depth of 6 or 8 
inches. The weights of all the materials going into the cupola should be 
kept separately. The melter should be furnished each day with a charging 
schedule giving the composition and the weight of each charge. 

The fire should be started about two hours before the blast is put on, 
to allow the charges in the stack to become well heated. The openings 
in the wind box are closed immediately after starting the blast. 

The egg-shaped section at the melting zone, which the cupola gradually 
assumes by use, should be maintained. 

The Charging Floor 

The charging floor should be large enough, if circumstances permit, to 
accommodate all the materials for the heat. Each charge of pig iron 
and scrap, after weighing, should be piled by itself and in the order in 



454 



The Cupola 



which it is to be used. The proper amount of coke for each charge is 
placed in cans or baskets. In larger works where the material is brought 

to the platform on charging cars, the 
cars are arranged so as to reach the 
cupola in proper order. 

The cuts show two different meth- 
ods of charging at large foundries. 
At one the charging is done by hand 
and at the other by machine. 

While the material is handled more 
rapidly and at less expense by the 
latter method, it is doubtful if the 
saving effected compensates for irregular melting and lack of uniformity 
in product, which is likely to result from unequal distribution of the 
charges. 




125 



Charging Floor. 




Fig. 126. — Cupola Charging Machine 
in Normal Position. 



Fig. 127. — Cupola Charging Machine 
in Charging Position. 



Melting Losses 

Melting losses in a well-managed cupola should not exceed 4 per cent 
for the annual average. Instances are known where the losses for long 
periods were not over 2 per cent. The following records are taken from 
the report of the secretary of the American Foundrymen's Association, 
and cover the results from 41 cupolas. The percentage of castings 
made and the returns are calculated from the quantities given and added 
to each table. 



Light Jobbing 
Table I. — General Jobbing 



455- 



Numbers 



Usual tonnage 

Time melting 

Blast pressure 

Fan or blower 

Pig iron 

Per cent southern 

Fuel used , lbs 

Scrap bought 

Pig iron used 

Scrap used 

Castings made 

Scrap made 

Per cent melting lost 

Per cent melt in returns . . . . 
Per cent in good castings . . . 



I hr. 15 m, 
8 oz. 
Fan 
Coke 
None 
Coke 
Mach. 
10,400 
9,600 
i6,49S 
1,352 
10.7 
66 
82.4 



3 

hr. 



Fan 
Coke 

Coke 
Med. mach 
3200 
3200 
5504 
620 
4-3 
97 
86 



3 


4 


3 


3 


ihr. 15 m. 


2hrs. 




80Z. 


Fan 


Blower 


Coke 


Coke 


None 


None 


Coke 


Coke 


Mach. 


Stove 


2657 


268s 


2886 


3885 


3916 


4057 


872 


1873 


13.6 


9-7 


IS. 7 


28. 5 


70.6 


61.7 



80Z. 
Fan 



Mach. 
20,000 
20,000 
3S.200 
2,200 
6.5 
6.5 



Average melting loss 7-6 per cent 

Average of melt in returns 8.8 per cent 

Average of melt in good castings 83.0 per cent 



Table II. — Light Jobbing 



Numbers 



Usual tonnage 

Time of melting 

Blast pressure, oz 

Fan or blower 

Pig iron 

Per cent southern 

Fuel used 

Scrap bought 

Pig iron used, lbs 

Scrap used, lbs 

Castings made 

Scrap made 

Per cent melting loss 

Per cent melt in returns. . 
Per cent in good castings . 



72 

3 hrs. 30 m, 

13 

Blower 

Coke 

None 

Coke 



102,000 

42,000 
108,300 
27,500 
5.7 
19. 1 
75-2 



I hr. 30 m. 
6.5 
Fan 
Coke 
None 
Coke & coal 
Stove 
4.500 
7,500 
10,300 
1,200 
4.2 
10 
85.8 



16 
2 hrs. 30 m. 

Fan 

Coke 

None 

Coke 

Lt. mach. 

19,200 

12,800 

21,000 

9,100 

6 

28.4 
65.6 



2.5 
Ihr. 



Fan 
Coke 
None 
Coke 
Med. mach. 
3200 
1800 
4000 
800 
4 
16 
80 



Average melting loss 25.5 per cent 

Average of melt in returns 20.8 per cent 

Average of melt in good' castings 73-6 per cent 



456 



The Cupola 
Table III. — Light Machineey 



Numbers . 



Usual tonnage 

Time of melting 

Blast presstire, oz 

Fan or blower 

Pig iron 

Per cent southern 

Fuel used 

Scrap bought 

Pig iron used, lbs 

Scrap iron used, lbs. 

Castings made 

Scrap made 

Per cent melting loss 

Per cent melt in returns 

Per cent melt in good castings . 



lo 
I hr. lo m. 



6 

2 hrs. 



Fan 
Coke 



Coke & coal 
None 
i6,ooo 
4,ooo 
13.220 
4,500 
6.5? 
22.6 
66.1 



Fan 
Coke & ch. coal 

Coke 
Med. mach. 
6,000 
6,000 
10,000 
900 
9.2 
7.5 
83.3 



35 

I hr. 30 m. 
7 
Blower 
Coke 
None 
Coke 
Lt. mach. 
3900 
2750 
3738 
2762 
2.3 
41-5 
56.20 





13 


14 


IS 






5 

I hr. 30 m. 

5 

Fan 

Coke 

50 

Coke & coal 

Med. mach. 

4500 

4280 

7640 

800 

3.9 

9-1 

87 


15 

2hr. 

7 

Blower 

Coke 

35 

Coke 
Lt. mach. 
14,000 
16,000 
20,500 
6,000 
II. 6 
20 
68.3 






6 hrs. 40 m. 




Fan or blower . 


Fan 




Coke 






Fuel used 


Coke 






Pig iron used, lbs. 


56,000 
24,000 


Scrap iron used, lbs. 




Scrap made 


16,000 


Per cent melting loss 


5 


Per cent melt in returns 


2,000 


Per cent melt in good castings 


75 



There is an error in this record. The loss should be 11.3 if the statement as to 
castings and scrap are correct. 

Average melting loss 7.33 per cent 

Average of melt in returns 19. 55 per cent 

Average of melt in good castings 73.0 per cent 



Stove Plate 
Table IV. — Heavy Machinery 



457 



Numbers ... ... 


i6 


17 


18 


19 






Usual tonnage 


13 
2 hrs. 

6 

Blower 

Coke 

5o 
Coke 
Mach. 
14,720 
11,130 
18,845 
4,870 
8.4 
18.8 
72.9 


15 

2 hrs. 

10 

Blower 

Coke 

70 

Coke 

H'vy mach. 

20,000 

10,000 

21,300 

7,200 

5 

24 

71 


21 
4 hrs. 

9 
Blower 
Coke & coal 
17 
Coke 
Mach. 
25,740 
16,270 
37,760 
7,560 
4 
18 
78 


15 


Time of melt 


2 hrs. 


Blast pressure, oz. 


14 


Fan or blower 


Blower 


Pig iron 

Per cent southern 


Coke 
20 


Fuel used 


Coke 


Scrap bought 




Pig iron used, lbs. 


15,500 


Scrap used lbs. 


11,500 












7-4 


Per cent melt in returns 

Per cent melt in good castings . 


22.2 
70.4 



Average melting loss 5-8 per cent 

Average of melt in returns 20 . 6 per cent 

Average of melt in good castings 73 . 6 per cent 



Table V. — Stove Plate 



Numbers . 



Usual tonnage 

Time of melt 

Blast pressure, oz 

Fan or blower 

Pig iron 

Per cent southern 

Fuel used 

Scrap bought 

Pig iron used, lbs 

Scrap used, lbs 

Castings made 

Scrap made 

Per cent melting loss 

Per cent melt in returns 

Per cent melt in» good castings . 



2 hrs. 15 min. 
14 
Blower 
Coke 
100 
Coke and coal 
Stove 
20,000 
20,000 
24,000 
14,200 
4-5 
35.5 
60 



15 

I hr. 30 min. 



II 



Coke 

50 
Coke 
Stove 
18,000 
12,000 
20,192 
9,000 
2.7 

30 

67.3 



13 

Blower 

Coke 

25 

Coke and coal 



11,863 
7,906 

11.750 
7,624 



38.5 
59-4 



Average melting loss 3.3 per cent 

Average of melt in returns 34- 3 per cent 

Average of melt in good castings 62 . 3 per cent 



45^ 



The Cupola 
Table VI. — Sanitary Ware 





23 


24- 


25 


26 








12 

2 hrs. 

5 

Fan 

Coke 

None 

Coal and coke 

Medium 

ii,8oo 

I2,200 

17,228 

6,048 

3 

25.4 
71.7 


32 

3 hr. IS m. 

14 

Blower 

Coke 


38 
3 h. IS m. 

14 
Blower 
Coke 

60 
Coke 
None 
56,000 
20,000 
51,614 
18,386 
7.9 
24.1 
67.9 


16 


Time of heat 

Blast pressure, oz. 


2 h. 30 m. 
SO 
Fan 






Coke 








Coke 










51,000 
12,000 
46,660 
12,234 
6.5 

19.4 

74 


9.875 
22,625 


Scrap used, lbs 


Castings made 


23,276 


Scrap made 


8,055 


Per cent melting loss 

Per cent melt in retioms 

Per cent in melt good castings 


3.6 

24.7 
71.6 



Numbers 


27 


28 


29 


30 






Usual tonnage 


. 25 

3 h. 45 m. 

14 

Blower 

Coke 


26 
3 h. 45 m. 


40 
3 h. 45 m. 
5 
Fan 
Coke 
None 
Coal and coke 
Medium 
35,560 
47.210 
S9.400 
21,960 
1.7 
26.5 
71.7 


23 


Time of heat 


3I1. 






Fan or blower , 

Pig iron 


Blower 
Coke 


Blower 
Coke 


Per cent southern 






Coke 

None 

31,470 

17.960 

35.956 

11,270 

4.1 

22.9 

73 


Coke 


Coke 


Scrap bought 


None 




33,000 
19.850 
37,250 
11,300 
8.1 

21.3 

70 


29,000 




17.500 




33.385 




11,500 


Per cent melting loss 

Per cent melt in returns 

Per cent melt in good castings 


3.5 
24.7 
71.8 



Average melting loss . 

Average of melt in returns 

Average of melt in good castings. 



4 . 84 per cent 
23.60 per cent 
71.50 per cent 



Railroad Castings 
Table VII. — Agricultural 



459 



Numbers 


31 


32 


33 


34 


35 






Usual tonnage .... 


80 

4 h. 20 m. 

15 

Blower 

Coke 

50 

Coke 

Ag. No. I 

80,000 

80,000 

108,800 

42,700 

5.3 

26.7 

67.5 


45 

3 h. 15 m. 

12 

Blower 

Coke 

' Coke ' 

Ag. No. I 

45,000 

45, 000 

61,200 

24,300 

5.2 

27 

67.7 


41 

3 h. 30 m. 

13 

Blower 

Coke 

50 

Coke 

Med. Mach. 

45,700 

35,800. 

62,960 

15,600 

3.6 

19.2 

77.2 


9 
2 hrs. 

12 

Blower 

Coke 

50 

Coke & coal 

Stove 

7,071 

10,674 

11.845 

5,200 

4 

29.3 

67 


9-5 
I h. 20 m 


Time of heat 


Blast pressure, oz 

Fan or blower . 


9 

Blower 


Pig iron 


Coke 


Per cent southern 

Fuel used 


None 
Coke & coal 


Scrap bought 

Pig iron used, lbs 

Scrap used, lbs. . 


Stove 
7,500 
11,600 






Per cent melting loss . . . 

Per cent melt in returns 

Per cent melt in good 

castings 


5.3 

55.7 

39 



Average loss in melt 4. 77 per cent 

Average of melt in returns •. 26. 73 per cent 

Average of melt in good castings 68 . 4 per cent 



Table VIIL — Railroad Castings 



Numbers . 



38 



Usual tonnage 

Time of heat 

Blast pressure, oz 

Fan or blower 

Pig iron 

Per cent southern 

Fuel used • 

Scrap bought 

Pig iron used 

Scrap used 

Castings made 

Scrap made 

Per cent melting loss 

Per cent of melt in returns . . . . 
Per cent melt in good castings . 



47 
5 hrs. 20 m. 

16 
Blower 
Coke 
None 
Coke 
None 
66,500 
28,500 
60,400 
28,900 
6.1 

30.3 

63.5 



32 


6.5 


3 hrs. 45 m. 


2 hrs. 


4 


9 


Fan 




Ch., coal and coke 


Coke 


60 


None 


Coke and coal 


Coke 


None 




25,000 


6,76s 


39.000 


6,235 


54,000 


10,000 


7,500 


2,38s 


3.9 


4-7 


II. 7 


18.3 


84.3 


76.9 



Note. — No. 37 is an average of 27 heats. No. 38 is an average of 25 heats. 

Average melting loss 5 . 64 per cent 

Average of melt in returns 22 . 43 per cent 

Average of melt in good castings 72.22 per cent 



460 



The Cupola 
Table IX. — Floor Plates, Grate Bars, etc. 





39 


40 




Usual tonnage 


30 

3 hrs. 40 m. 
16 
Blower 
Coke 
None 
Coke 
Med. mach. 
20,000 
40,000 
47,400 
8,200 
7.3 
13-7 
79 


3 


Time of heat 


I hr. 


Blast pressure, oz 




Fan or blower 


Fan 


Pig iron 


Coke 


Per cent southern 




Fuel used 


Coke and coal 


Scrap bought 


Light mach. 


Pig iron used, lbs 


None 


Scrap used, lbs 


6,000 


Castings made ... . 


5,100 




525 




6.2 




8.8 




85 







Average melting loss 

Average of melt in returns 

Average of melt in good castings . 



7 . 23 per cent 

8 . 88 per cent 
85 per cent 



Table X. — 


Car Wheels 




Number 


41 


Number 


41 








Usual tonnage 


200 

7 hrs. 

10 
Blower 


Scrap bought 


Wheel 


Time of heat 


Per cent melting loss 


2.1 




Per cent melt in returns 

Per cent melt in good castings. 




Fan or blower 





From the above tables, the following table showing the average results 
for each class of work is compiled. 

Table XI 



Percentage 


1^ 

St 




3't 




0. 

I 

o5 


si 

CO 




< 


13 


It 




Number of records. 
Per cent melt in 


4 

83.9 
8.2 

7-7 


4 

73.6 
20.8 

55 


6 

73.01 

19 SS 
7.33 


4 

73.6 

20.6 
5.8 


3 

62.3 

34.3 
3.3 


8 
71. 5 

23.6 
4.84 


5 
68.5 

26.7 

4.77 


3 

72.3 

22.43 
5.24 


2 

79-5 

13.2 
7.2 


rt 
!§ 


Per cent melt in 





Per cent melt lost . 





Note. No. 12 was omitted in obtaining these averages. Evidently there was 
something wrong about this heat as shown by the excessive returns. 



Melting Ratio 461 

The figures in the preceding table are to be taken as approximations. 
The loss may be reduced in practice by careful management. 

When the weight of the coke on the bed, and the weights of the iron 
and coke in each charge are known, to determine the necessary amount 
of iron which must be melted to produce a desired melting ratio: 

Let X = the total iron; 
Y = the total coke; 
A = weight of coke on bed; 
B = weight of coke in each charge; 
C = weight of iron in each charge; 
D = the desired melting ratio. 

(i) Then f = D, F = ^ total coke (2) 

(3) and -f; = the number of charges. 
The total coke is found in equation (4) 

(4) Y = {.^-i^B+A. 



From equations (2) and (4) X = -~ — =-ir-^ 

C — DB 



(5) 



Having found the total amount of iron, the total coke and number of 
charges are found from (2) and (3). 

By applying these formulas to a 54-inch cupola as given in table on 
pp. 451-2 the required weight of iron to be melted to produce a melting 
ratio of 9 to I may be found. 

Melting Ratio 

Weight of coke on bed ^ = 1100 pounds 

Weight of coke to each charge B = 180 pounds 

Weight of iron to each charge C = 1900 pounds 

Required melting ratio Z) = 9 to i pounds 

From equation (5) 

1900 X 9 (iioo — 180) . ^ 

^ ^ 1900 - 9 X 180 = 56,185, 

Y = — = 6243 pounds. 

And the nimiber of charges 

56,185 

^-^-^ = 29.57. 
1900 ^^' 

Coke may be charged from dumps, as it can be uniformly spread. 



462 The Cupola 

The cupola should be kept full to the charging door until all the iron 
is in. Later the sweepings from the charging platform may be thrown 
on. The platform should, if possible, be large enough to accommodate 
the materials for the entire melt. Each charge of pig and scrap should 
be weighed and piled by itself; the coke kept in convenient charging 
buckets, and the broken limestone in a bin from which it may be charged 
by measure, above the coke. 

Appliances about Cupola 

The conditions will indicate the necessity for elevator and charging 
cars. In every foundry yard there should be a cinder mill and scrap 
breaker. In many foundries the cinders are frequently ground in the 
tumbling barrel. It is purely a matter of convenience; but locating 
the cinder mill in the yard promotes cleanliness, especially when broken 
fire brick are ground. 

The cinder mill is made up of cast-iron staves from 8 to 10 inches wide 
and of convenient length, placed about polygonal heads; the latter 
mounted on trunnions, and the whole rotated slowly by any suitable 
means. The staves are so placed that there is not over an eighth of an 
inch opening at the joints, in order that the shot iron may not escape. 
Magnetic and hydraulic separators are frequently used to recover the 
shot, and they effect large savings. 

The scrap breaker is located conveniently to the cars, or placed 
where heavy scrap is received. It consists of a derrick and ball with 
hoisting apparatus. The height of the derrick should be from 30 to 
40 feet and the ball should weigh 2500 to 3000 pounds, both depending 

on the probable dimensions of the 
largest scrap. 

The sketch below shows a simple 
and effective device for tripping the 
ball. 

Ladles 

Hand ladles, and shank ladles 

holding 200 pounds or less, are best 

' y-v % made of sheet steel, as they are 

f \ \ much lighter and are easily repaired. 

A // These, as well as larger sizes, to be 

handled by cranes, are furnished by 
Fig. 128. , . / , ■, 

the foundry supply nouses. 

It is usually best to tap into a fore ladle. This is kept under the 

spout, and has sufficient capacity to hold one entire charge. From it 




© 



The Bod Stick 463 

the smaller ladles are filled. By making large tappings, the various 
grades of iron in the cupola become thoroughly mixed in the fore ladle. 
The iron in the ladle is kept hot by covering the surface with charcoal 
or slacked lime. 

In English practice the Fore Hearth is largely used instead of the fore 
ladle, but its use has not met with favor in the United States. An illus- 
tration of this arrangement is shown on page 248 of McWilliams and 
Longmuir's General Foundry Practice. 

Lining of Ladles 

The ladles are lined with a mixture of one-half fire clay and one-half 
sharp sand. With small ladles the lining is from % inch to iH inches 
thick on the bottom and gradually tapers to 14 to % inch thick at the 
top. 

Large ladles have first a lining of fire brick, then the clay daubing. 

After the linings are completed they must be thoroughly baked either 
by placing the ladles in an oven or by building wood fires in them. It 
is customary to reline the small ladles after each heat. The larger ones, 
if completely drained of iron, may, by chipping out and patching, be 
made to last over many heats. The skulls from ladles are rattled with 
the cinders. Shanks for ladles holding 100 pounds and upwards are 
commonly made with single and double ends. The better practice is 
to make both ends double, the helper's end having a swivel joint. With 
this type of shank the helper can use both hands in carrying and two 
men can handle a 200-pound ladle easily. The iron bottoms of the 
larger ladles should have 10 or 12-%-inch holes through them to permit 
the escape of moisture. 

Tapping Bar 

The tapping bar is usually made of i-inch gas pipe, having a long 
tapered point (24 inches in length) welded to it at one end. Frequently 
the tapper stands along one side of the spout, and opens the tap hole 
with a single-handed bar. He carefully picks away the center of the 
bod, until a hole is made through it, then enlarges the hole to ¥s inch, or 
an inch, according to the stream desired. 

The Bod Stick 

The bod stick is an iron bar about i inch in diameter, having at one 
end a flat disc 2H inches in diameter. To this disc is attached the 
clay bod, used in stopping up the tap hole. In stopping the stream 
of iron, the bod, placed above the stream at the tap hole, is forced down- 



464 The Cupola 

Table Showing Capacities of Ladles with Bottom Diameters 



Depth 


Diameter of ladle at bottom, inches 


20 


22 


24 


26 


28 


30 


32 


34 


36 


Ins. 
2 

4 ■ 
6 
8 
10 
12 
14 
16 
18 
20 
22 
24 
26 

30 
32 
34 
36 
38 
- 40 
42 
44 
46 


157 
318 
483 
652 
825 
1002 
1 183 
1368 
1557 
1749 
1946 
2149 


191 
334 
585 
788 
997 
1210 
1427 
1648 
1873 
2102 
2337 
2576 
2821 


227 

459 

696 

938 

1 185 

1436 

1693 

1954 

2221 

2492 

2769 

3050 

3337 

3630 


267 
538 
815 
1096 
1383 
1676 
1973 
2276 
2585 
2900 
3221 
3548 
3880 
4218 
4560 


309 
624 
945 
1272 
1604 
1942 
2286 
2606 
2992 
3353 
3720 
4093 
4472 
4807 
5248 
5645 


356 
717 
1084 
1457 
1836 

2221 
2612 
3009 
3412 
3821 
4237 
4660 
5089 
5525 
5968 
6417 
6871 
7329 


403 
812 
1228 
1651 
2080 
2516 
3142 
3408 
3863 
4325 

4793 
5268 
5750 
6238 
6734 
7237 
7747 
8261 
8781 


455 
917 
1,385 
1,860 
2,342 
2,830 
3,326 
3,829 
4,339 
4,855 
5.378 
5,911 
6,451 
6.998 
7.552 
8,114 
9,682 
9,258 
9,840 
10.42S 


510 
1,026 
1,550 
2,08s 
2,62s 
3.172 
3.726 
4,288 
4.856 
5.432 
6,016 
6,608 
7.208 
7.816 
8,432 
9,054 
9,694 
10,332 
10,978 
11,630 
12,288 


48 


For steel add 5% 


50 

52 

54 
56 
58 
60 
62 
64 
66 
68 























wards into the hole squeezing off the stream. Many severe burns have 
been caused by stopping directly against the stream. 

The spout is sometimes made with a side opening to carry off slag 
running on the stream of iron. This opening is made about the middle 
of the spout, and the trough in that vicinity is somewhat increased in 
width. About 2 inches below the side opening a fire brick is placed 
across the trough, leaving room below it for the iron to pass, but 
being low enough to skim off the slag, which runs out of the side at 
the opening. A swinging spout is occasionally used. This is hung 
on a pivot below the spout proper, and in a transverse direction. 



Capacities of Ladles 465 

Varying from 20 to 54 Inches, Slope of Sides iVz to i Foot 









Diameter of ladle at bottom, inches 






Depth 




















38 


40 


42 


44 


46 


48 


50 


52 


54 


Ins. 




















2 


568 


630 


694 


762 


832 


906 


984 


1,064 


1,146 


4 


1,144 


1,268 


1,396 


1,600 


1,672 


1,820 


1,978 


2,138 


2,302 


6 


1,728 


1,914 


2,106 


2,310 


2,522 


2,774 


2,982 


3,222 


3,469 


8 


2,330 


2,568 


2,824 


3,096 


3,380 


3.678 


3,996 


4,316 


4,829 


10 


2,930 


3,330 


3,552 


3,892 


4,248 


4,622 


5.019 


5,420 


6,063 


12 


3,538 


3,900 


4,288 


4,696 


5,124 


5,576 


6,052 


6,334 


7,308 


14 


4,154 


- 4,578 


5,032 


5,510 


6,012 


6,540 


7.095 


7,659 


8,564 


16 


4,776 


5,264 


5,784 


6,332 


6,910 


7,514 


8,149 


8,784 


9,831 


18 


5,406 


5,958 


6,546 


7,154 


7,816 


8,498 


9.213 


9.930 


10,711 


20 


6,044 


6.660 


7,316 


7,994 


8,730 


9.492 


10,287 


11,086 


11,936 


22 


6,690 


7,370 


8,094 


8,844 


9,6S4 


10,496 


11,371 


12,253 


13,212 


24 


7,344 


8,088 


8,880 


9,702 


10,588 


11,510 


12,465 


13.422 


14,479 


26 


8,C5o6 


8,816 


9,676 


10,570 


11,532 


12,533 


13.569 


14.623 


15,757 


28 


8,676 


9,552 


10,480 


11,446 


12,486 


13.566 


14,683 


15,826 


17,046 


30 


9.354 


10,296 


11,294 


12,334 


13.450 


I4,6c9 


15,808 


17,038 


18,346 


32 


10,040 


11,048 


12,116 


13,232 


14,424 


15,663 


16,943 


18,261 


19.657 


34 


10,734 


11,810 


13,943 


14,140 


15,408 


16,727 


18,089 


19.495 


20,979 


36 


11.436 


13,580 


.13,788 


15,059 


16,402 


17,801 


19,249 


20,740 


22,312 


38 


12,146 


13,358 


14,618 


15,988 


17,406 


18,885 


20,412 


21,996 


23,657 


40 


12,864 


14,144 


15.496 


16,927 


18,420 


19.998 


21,591 ' 


23,263 


25,014 


42 


13,590 


14,940 


16,364 


17,876 


19,443 


21,083 


22,782 


24,541 


27,070 


44 


14,322 


15,712 


17,240 


18,83s 


20,476 


22,197 


23,98s 


25,830 


27,761 


45 




16,550 


18,122 
19,014 


19,802 
20,776 
22,198 


21,519 
22,573 
23,637 


23,322 

24,557 
25,703 


25,197 
26,420 
27,654 


27.130 
28,441 
29,763 


29,152 


48 


For steel add 5% 


30,55s 


50 






31,920 


52 










24,711 


26,859 


28,899 


31,096 


33,397 


54 












28,032 


30,155 


32,441 


34,336 


56 












29,223 


31,422 


33,798 


36,287 


58 












30,256 


32,690 


35,166 


37,750 


60 














33,979 


36,545 


39.225 


62 














35,279 


37,941 
39,343 
42,312 


40.712 


64 
66 


The foundry 


42,211 
43.729 


68 














46,011 



While the stream is running it can be tipped so as to let the iron 
run into a ladle at either side. In rapid melting this obviates stop- 
ping up when ladles are changed. 



Applying Metalloids in Ladle 

Where metalloids are added to the iron, if the amount to be used is 
sprinkled into the stream as it flows through the spout, a more intimate 
mixture is obtained than results from placing the material in the ladle 
and drawing the iron on to it. 



466 



The Cupola 



Cranes 

The equipment of cranes as to size, style and motive power is indi- 
cated entirely by the character and volume of production. Ample and 
convenient hoisting facilities are absolutely essential. A mistake is 
seldom made in providing cranes of too great capacity. 

Most of the modem foundries are fitted with electric traveling cranes, 
which not only have access to the cupola, but sweep over the moulding 
floors. In addition to the electric crane, post and wall cranes are 
supplied for special requirements. There should be a small jib crane 
attached to the cupola for handling the fore ladle. 

The manufacture of cranes has become a specialty, and the reader is 
referred to manufacturers' catalogues for special information. 



Spill Bed 

In many foundries the excess iron, and iron on the bench floor, is 
frequently dumped into holes in the sand heaps or floors. This is a 
slovenly practice and greatly injures the sand. 

A very convenient and simple spill bed is shown in Fig. 129. This 
is so made that the iron is collected in pieces weighing from 60 pounds to 
80 pounds, of convenient size to be handled in charging. 

A small bed of same character serves an excellent purpose when placed 
near the snap floors. 



Dumping Spill Bed 




Fig. 129. 



Gagger Mould 
Gagger Mould 



467 




Fig. 



130. 



By a little care all the excess iron may be put through beds as above 
and sent to the cupola in good shape for melting. 

The usual practice is to allow the bottom to remain where it drops 
until the next morning, simply wetting it thoroughly. 

Below is shown a sketch of a large rake. If the bottom is dropped 
on this and the mass pulled out from under the cupola (by means of a 




Fig. 131. 

chain passing through a snatch block to the crane) and then wetted 
down, it will be found in much better shape for picking over in the 
morning. 

The pieces of unconsumed coke should be picked out and used in 
core ovens, or as part of the last charge of coke, in the cupola. Little 
savings of this kind, although small of themselves, amount to an impor- 
tant item in the course of the year, particularly if the operations are 
extensive. 



CHAPTER XX 
MOULDING SAND 

Moulding sand contains from 75 to 85 per cent silica, with varying 
proportions of alumina, magnesia, lime and iron. 
The essential properties are: 

Cohesion, Refractoriness, 

Permeability, Durability, 

Porosity, Texture. 

Cohesion or Bonding Power 

Moulding sand must possess sufficient cohesion, not only to remain 
in position after ramming, but to resist the pressure of the molten 
metal, and its abraiding action while being poured. 

Pure sand has no cohesive strength, but clay (double silicate of 
almnina) has, and as moist sands cohere more strongly than dry, 
the bonding power must depend on the amount of clayey matter and 
water contained. The moisture must not be in excess, otherwise the 
sand will pack too densely. 

Permeability and Porosity 

Permeability is the property which sand possesses of allowing liquids 
or gases to filter through it, and depends on the size of the pores. 
By porosity is meant the volume of pore space. 
These properties are not the same. A sand may contain a few large 
openings through which the liquids or gases may readily escape and yet 
have a small pore space. On the other hand, the total pore space may 
be large, but by reason of the small size of the pores, permeability by 
either liquids or gases might be difficult. 
The permeability of sand may be influenced: 
By the tightness of packing; 
By the size of the grains; 
By the fluxing elements in the sand. 
By tamping or packing, the space occupied by a given weight of 
sand may be reduced, as the grains are forced into their closest arrange- 
ment producing the minimum pore space. Fine-grained sands have 
larger pore space than coarse-grained. 

468 



Texture 469 

If silt or clay are present, and segregated, the sand will pack more 
closely than if the grains are cemented together in the form of com- 
poimd grains. In the latter case the permeability and porosity would 
be larger than if the grains were separate. 

The decreased permeability under increased tamping explains why 
some good sands behave badly. Permeability of sand is also influenced 
by the amount of water present. The relation between permeability 
and fluxing impurities is shown in the process of casting. If the clayey 
particles filling the interstices of the sand fuse when heated by the metal, 
their coalescence in melting will close up the pores to some extent. For 
this reason, in part, a high percentage of fluxing impurities is undesirable. 

The proper permeability of a moulding sand is a matter of vital 
importance. A pathway must be opened for the escape of the gases 
to avoid blowing. The finer the sand the lower its permeability. 

Refractoriness 

A moulding sand must be sufficiently refractory to prevent complete 
fusion in contact with molten metal. Highly siliceous sands are, there- 
fore, the more desirable. At the same time a high percentage of silica is 
gained at the expense of alumina and a consequent loss of bonding power. 
Generally silica should not exceed 85 per cent. Silica is refractory, does 
not shrink when heated, but has no cohesive nor bonding power. 

Alumina, a most important component, is present in moulding sands 
in amounts varying from 4 to 12 per cent. It is refractory, has great 
bonding power, but shrinks greatly when heated. Too high a percentage 
of alumina makes the sand impermeable. 

Durability 

Sands begin to lose some of their desirable qualities after one or 
more heats and become dead or rotten. The injury to the sand arises 
from its dehydration, or loss of combined water by the heat of the molten 
metal, whereby its bonding power is destroyed. The water of com- 
bination cannot be restored. 

The amount of sand burned is a layer of varying thickness next to 
the casting. 

Texture 

By texture is meant the percentage of grains of different sizes. This 
is determined by passing the sand through a series of sieves of decreas- 
ing mesh and noting the percentage remaining on each sieve. Mr. W. 
G. Scott pursues the following method: 

"Ten grams of sand are placed on the loo-mesh sieve, together with 
ten jie steel balls, and shaken with a circular motion for one minute. 



470 



Moulding Sand 



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fe« 



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Texture 



471 



The sand passing through is weighed and credited to the 100- mesh sieve. 
That which remains, together with the balls, is emptied on the 80-mesh 
sieve and the operation repeated. In like manner sieves of varying 
size up to 20 mesh are used. The preceding table shows the texture or 
sand from different localities. " 

Lime is a fluxing element. If present as a carbonate, it loses its 
carbonic acid under heat, and in excessive amount the gas causes the 
mould to flake or crumble. Caustic lime fluxes and forms slag on sur- 
face of castings. 

Magnesia is also a flux, and to a modified extent has the effect of hme. 

Iron, as a carbonate or an oxide, if present in the mould near the 
casting, is converted into ferrous oxide, which is a flux. 

Combined water is present in all sands containing clay, carbonate of 
lime or gypsum. It is driven off at a low red heat and increases the 
porosity of the sand. 

Moulding sands are not always used alone. One or more grades are 
frequently mixed together. Blending is extensively practiced at the 
pit as well as at the foundry. In addition to blending to increase cer- 
tain physical properties, foreign substances, such as ground coal, graph- 
ite, molasses, flour, beer, linseed oil or cinders are used, either to increase 
the bonding power or permeability of the material. A sand deficient 
in its natural condition" may be greatly improved by "doctoring." 
The sand from any one deposit does not always run uniformly, and with- 
out previous careful examination of the shipments, unfavorable results 
may appear in the foundry. 

The following table, taken from "The Iron Age," gives the analysis 
of eight different samples. 



Constituents 



Silica 

Alumina 

Ferric oxide . . . . 

Lime 

Magnesia 

Potash 

Soda 

Water 

Organic matter. 



92.08 
5. 41 
2.49 



91.90 

5.68 

2.17 

.41 



92.91 

5.85 
1.24 



90.62 
6.66 
2.70 



81.50 
9.88 
3.14 

1.04 
.65 



84 



82.90 
21 
90 
62 



85 



79.81 

10.00 

4.44 

.70 



2.89 



Sands which contain the largest percentage of silica, sufficient alimiina 
to impart cohesiveness and plasticity, with from i to 3 per cent of 
magnesia are the best for facing. Such sand should be entirely free 
from lime. 



472 



Moulding Sand 



Specifications of W: G. Scott, Racine, Wis. 

"Moulding sand for iron work generally contains from 75 to 85 per 

cent of silica; 5 to 13 per cent of alumina; less than 2.5 per cent lime 

and magnesia; not over 0,75 per cent soda and potash and generally 

less than 5 per cent oxide of iron; not more than 4 per cent of water. " 

Sand for Brass 

Sand for brass may contain a much higher percentage of iron and 
lime without detriment. 

All moulding sands contain more or less organic matter. Carbonate 
of lime must not exceed 1.5 per cent for iron sands, nor 234 per cent for 
brass. Iron oxide must not exceed 5.5 per cent for iron nor 7 per cent 
for brass sand; organic matter not to exceed i per cent. Any sand 
showing an excess of 13 per cent alumina will be rejected. 

Analysis 



Constituents 



SUica... 

Alumina 

Iron oxide 

Lime... 

Lime carbonate . 



Soda 

Potash; 

Manganese 

Combined water. 
Organic matter . . . 
Specific gravity . . 
Fineness 



For light 
iron work 



82.21 
948 
4.2s 



2.64 

.28 

2.652 

85.18 



For 
medium 
iron work 



85.85 

8.27 

2.32 

.50 

.29 

.81 

.10 

.03 

Trace 

1.68 

.15 

2.654 

66.01 



For heavy 
iron work 



6.30 

2.00 

.78 



.50 



.25 
1.73 

.04 

2.63 

46.86 



For light 
brass 



78.86 

7.89 

S.45 

• SO 

1.46 

1. 18 

.13 

.09 

Trace 

3.80 

.64 

2.64 

94.88 



Any of these sands would answer very well so far as their chemical 
composition is concerned, for any class of work; but it is absolutely 
necessary that they should possess the proper degree of fineness. 

The finer sands are less siliceous and as a rule carrj' higher percentages 
of almnina and fluxes than coarser grades, as shown by the following 
table. 



Size 


60 


80 


TOO 


100 


Silica 


95.92 

1.29 

.56 

.10 

2.13 

97.87 


94.35 

1.47 

.56 

.04 

3.58 

96.42 


94.66 

1.47 

.40 

.34 

3.13 

96.87 


91.06 




4.57 


Ferric oxide 


.80 


Lime 


72 


Alkalies 


2 8s 


Total 


97.15 





Testing Moulding Sand 473 

The greater the average fineness, the lower the permeability. 

Prof. Ries, from whose paper the above notes are extracted, concludes 
that the chemical analysis of moulding sands are not of as much impor- 
tance as their physical properties. 

To test the "temper" and strength of sand, the moulder squeezes 
a handful into a ball. If it takes the impression of his hand readily 
and leaves the hand clean, it is considered sufficiently damp. Its 
strength or binding power is tested by lifting the lump from one end, 
or by carefully breaking it apart; or he may squeeze a ball of sand about 
a little stick or nail and see if it can be lifted by the stick. He then 
blows through it to test its porosity. Such crude tests are in constant 
use and, conducted by experienced moulders, serve the purpose. 

A. E. Outerbridge instituted a series of experiments to determine 
these characteristics more definitely. The following is extracted from a 
paper read before A.S.M.E., at their New York meeting in 1907. 

"A number of test bars of green sand 6" X i" X 1" were made 
imder uniform conditions of pressure, dampness and quality of material 
used in forming the ordinary mould. These little test bars were placed 
upon a smooth metal plate with sharp square edges. The bars were 
then pushed over the edge of the plate until they broke, when the amount 
of the overhang was measured. It was soon found that there was a 
great difference in the length of the overhang, which was regarded as 
a quantitative measure of the toughness of the sand. These differences 
were not even noticeable in the crude ball test. 

Samples taken from different parts of a small sand heap that had been 
uniformly dampened, or tempered, varied greatly in this respect, owing 
no doubt to the irregular distribution of the alumina or clay binder; 
and the correctness of this inference was subsequently confirmed by 
simple analytical tests. After a sufficient number of these test bars 
had been made and broken to prove the reliability of the method, further 
tests were devised to ascertain whether the usual methods of riddling 
and mixing the sand for the moulder's use affected its quality either by 
increasing or decreasing its toughness, as shown by the amount of over- 
hang of similar test bars of green sand. It was proved that the more 
thoroughly the sand was worked, the greater the overhang, due, as al- 
ready stated to the more uniform distribution of the binder. 

"The ideal moulding sand is a material in which the individual grains 
of silex, constituting approximately 90 per cent of the mass, are com- 
pletely covered with an overcoat of alumina or clay and the more 
uniform the grains are in size and shape, the better is the sand with 
respect to porosity in relation to the average size of the grain. 

"It was found on passing a sample of sand a number of times through 



474 



Moulding Sand 



a handriddle, and making test bars from the sample after each riddling, 
that the overhang was increased measurably. Thus, a sample of sand, 
which, after tempering and mixing by hand with a shovel, showed an 
overhang of less than two inches of the test bar, increased to nearly 
three inches after a dozen riddlings. It would not be practicable to 
treat large masses of sand in this manner, nevertheless, the informa- 
tion thus obtained was quite valuable and led to important practical 
results. 

"Another novel observation was concurrently made, viz., that the 
increased toughness and porosity noticed in these tests might be partly 
due to "aeration" or to the separation of the grains of sand when 
falling from the sieve to the floor. In order to discover the truth or 
falsity of this view, a quantity of sand was shaken in a box with a closed 
lid for several minutes and test bars were made before and after shaking. 
The correctness of the theory was quickly shown, for the shaking with- 
out sieving proved to be more effective than the sieving without shaking. 
Tests for porosity were also made, but these were not very satisfactory 
owing possibly to lack of suitable means of controlling and measuring 
the compressed air." 

Using one of Wm. Seller's & Co. 's centrifugal sand mixers, the develop- 
ment of which was largely due to Mr. Outerbridge's experiments, a series 
of tests were made with facing sand prepared as follows: 



Strong Sand 



Parts 



Strong Lumberton sand (new) 14 

Gravel (new) 7 

Flour sand (old) . 6 

Coal dust 2 




Fig. 132. — Green Sand Test Bars made from One Sample of Sand. 

"Fig. 132 is from a photograph showing eleven bars 6" X 1" X i", 
made from strong sand under uniform conditions of quantity, temper 
(dampness) and pressure. 



Testing Moulding Sand 475 

"The bar labeled o was pressed from a sample of the sand after 
having been dampened and turned over several times, with a shovel, 
and only partly mixed. The object of such preliminary mixing is 
simply to prevent the coal dust from flying out of the centrifugal ma- 
chine on subsequent treatment. 

"The other bars were made from the same pile of strong sand, after 
passing through the centrifugal machine from one to ten times. These 
bars were laid side by side upon the smooth metal plate, resting upon a 
table, and were slowly pushed over the edge of the plate until they 
broke." 

The following table gives the measurements of the overhang of each 
bar as nearly as the somewhat irregular shape of the break permitted. 

Inches 

214 

• ■■■ 3 

•• 3H 

3^ 

3H 

■ ■••• 3^ 

3H 

3% 

3^ 

3% 

• 3% 



No. length of overhang 


No. I 




No. 2 




No. 3 " 




No. 4 " 




No. 5 " 




No. 6 " 




No. 7 




No. 8 




No. 9 " 




No. 10 " 





"It will be observed that the first treatment increased the overhang 
% inch, the subsequent treatments increased the overhang in some 
cases H inch, and in some cases not measurably. The first treatment 
was, therefore, the most effective, and for practicable purposes one 
treatment is often sufficient to insure good mixing of the materials and 
thorough disintegration of any lumps. 

"The strain tending to break the sand beam is increased by the 
additional weight of the increasing length of the overhanging portion, 
and also by the increased moment of its center gravity. It is readily 
seen, therefore, that an increase in length of the overhang of % inch 
on the first treatment in the centrifugal machine means an increased 
tenacity of 75 per cent. In like manner an increase in overhang of 
50 per cent means an increase in strength of sand of 225 per cent. 

The illustration. Fig. 133, shows the fractured surfaces of the same 
bars. 

"Bar No. o shows the heterogeneous components of the partly mixed 
sand, while the other fractures show increasing uniformity due to more 
thorough mixing, and disintegration of lumps up to No. 3, after which 
no further increase in uniformity is observable to the eye. 



476 



Moulding Sand 




Fig. 133. — End View of the 
Test Bars in Fig. 132. 



The illustrations convey a very fair impression of the actual appearance 
of the bars. The appearance of the fractured surfaces coincides with 
the tests for overhang, and shows that a single treatment in this machine 

is in many cases sufficient, and two 
treatments are all that are usually 
needed with any sand mixtures. 

In mixing core sand containing flour, 
the effectiveness of this method is still 
more strikingly evident, owing to the 
almost total disappearance of the white 
flour, due to its thorough commingUng 
with the sand and coal in one treat- 
ment. 

The centrifugal machine is especially 
efficient in mixing sharp sand with lin- 
seed oil for cores. When so used it is 
run at a lower speed than when used for 
tempering and mixing moulding sand. 
Two treatments are sufficient to insure 
thorough mixing of sharp sand and oil for cores. 

There are many other devices for tempering and mixing sand mechan- 
ically, such as, shakers, revolving reels, etc., which are effective. 

The amoimt of cohesive matter, or binder, in moulding sand should be 
limited to that which will permit good ramming, without destroying its 
porosity, so that the gases will escape readily, without allowing the iron 
to penetrate. 

The sand in a mould next to the casting is burned and loses much or 
all of its cohesion. This is due to driving off the water of combination 
in the alumina which cannot be restored. The thickness of the layer 
of burned sand depends upon the size of the casting and temperature of 
same. 

It is impossible to separate all of this burned sand after the removal 
of the castings. Much of it gets mixed in the sand heaps, which must 
be strengthened from time to time with new sand . 

Aside from the loss of combined water and increase in iron content, 
chemical analysis shows little difference in the composition of new and 
burned sand. This is shown in the table on page 437, made by analyz- 
ing the same sand before and after using. 

In general, moulding sand must possess the following requirements. 
It must be sufficiently porous to allow the free passage of air and 
the gases generated in casting. 

It must resist high temperature without fusing. 



Moulding Sand Requirements 



477 



It must permit of easy removal from the cold castings. 

When rammed into shape it must, be firm and sufi&ciently compact 
to resist the pressure of the liquid metal. 

It must be strong enough to resist the abraiding action of the stream 
of metal entering the mould. 



Constituents 


New 


Burned 


Silica 


83.49 

7-25 

4.71 

.36 

.35 

1.30 

.41 

.30 

1.66 


82.32 

7.80 

3.98 

.54 

.41 

1.64 

.81 

.22 

.19 

2.38 

100.28 
60.80 










Potash 

Soda 


Titanic oxide 


Water 


Ferrous oxide 


Total 


99.86 
64.50 







For Dry Sand Moulding 

Any sand which, when rammed, will permit of drying into a compact, 
coherent but porous mass, will answer the purpose of a dry sand mix- 
ture. Many green sands dry into friable masses. 

Such sands must be mixed with some substance to give them strength. 
For such purpose, flour, stale beer, molasses-water, or clay-wash may 
be used. When flour is used, it is mixed in the proportion of one to 
twenty or thirty, depending upon the character' of the sand. 

With some sands the flour may be dispensed with and the sand 
strengthened sufficiently with molasses- water or clay wash. In dry 
sand moulds, only one or two inches of the sand next the pattern are of 
the prepared mixture. The remainder of the flask is filled with ordinary 
heap sand. This should be as open as possible to permit the ready 
escape of the gases. The facing should likewise be as open as can be 
safely worked. The amount of moisture should be about the same as is 
used in green sand. Dry sand facings must be thoroughly well mixed. 

Mr. West gives the following mixtures for dry sand facings. 

For Large Spur Gears p^j.^g 

Lake sand 12 

Strong loam sand 12 

Moulding sand 4 

Coke, amount i-io 

Flour iH 

Wet with water. 



47^ Moulding Sand 

Or Part 

Moulding sand i 

Jersey sand i 

Fire sand i 

Sea coal i-io 

Wet with thin clay wash. 

For Close Facing 

Moulding sand 6 

Lake or bank sand iJ^ 

Flour i-so 

Wet with clay wash. 

This mixture may be used for blacking, using flour 1-40. 

For Cylinders - 

Fair loam 4 

Lake sand i 

Sea coal or coal dust 1-14 

Wet with clay wash. 

General Work _ ^ 

Part 

Moulding sand i 

Bank sand i 

Flour 1-30 

Sea coal 1-20 

Wet with clay wash. 

Parts 

Strong loam sand 6 

Lake sand 6 

Old dry sand 2 

Flour 1-40 

Sea coal 1-14 

Wet with water. 

For Rolls 

Parts 

Dry sand 2 

Lake sand i 

Sea coal 1-12 

Flour 1-18 

Wet with clay wash. 

For Renewing Old Dry Sand for Body of Moulds p 

Old sand 16 

Lake sand 8 

New loam 4 

Wet with water. 



Or 



Core Sand 



479 



Dry Sand Moulds 

Old dry sand becomes very close. It should be passed through a 
No. 8 riddle to remove the dust and very fine particles. The coarse 
material mixed with new sand works well. 

Skin Drying 

Instead of making dry sand moulds which are baked in the oven, moulds 
are more frequently "skin dried." Skin dried moulds are essentially 
the same as "dry sand" except that the drying does not extend to as 
great depths and the facing is not as strong. 

For skin dried moulds mix with ordinary heap sand about i to 30 flour. 
After the mould is finished sprinkle with molasses water. The mould is 
dried either with the kerosene blow torch, or fire of wood, coke or char- 
coal, built in iron baskets which are placed in the mould. Often the 
mould is covered with sheet iron and fires are built on top of the iron. 
In drying copes, they are suspended and fires built under them." 

Before drying, the moulds are brushed with black wash, made of plum- 
bago and water, to which a little molasses water or clay wash is added. 
Sometimes moulds are black washed after drying. 



Core Sand 

Core sand should be high in silica and low in alumina. A sand con- 
taining much alumina does not permit the ready escape of gases after 
baking. 

Analyses of Core Sands 

(W. G. Scott) 



Constituents 


Good 

quality 

core sand 


Fair 
quality- 
core sand 


Silica 


94.30 

1.95 

.33 

1.63 


69.31 
4.76 
1.58 
3.50 
8.19 
7.77 
.12 
2.95 
1.82 


Alumina 


Iron oxide . . ... 


Lime carbonate 

Lime sulphate. 


Magnesia 

Alkalies 


.54 

.05 

1.05 

.15 


Combined water 

Organic matter 



"Since the greater portion of a core is to be entirely surrounded by 
metal, the sand of which it is composed encounters conditions much 



480 Moulding Sand 

more severe than those met with by facing sands. Three conditions 
must be noted. 

First. — The core is subjected to much handling. 

Second. — The gases generated in casting must find egress through 
the core and not through the metal. 

Third. — The core has finally to be removed from the casting. 

"All cores, before entering the mould, are dried, and in this condition 
must be hard enough to permit handling, and porous enough to admit 
the free escape of gases. Yet the sand must not be burned or converted 
into a compact mass by the heat; if so, it will be extremely difficult to 
remove from the casting. 

"A sand high in siUca should yield the best results. To such a sand 
the necessary bond must be added. An ideal core sand is one in which 
the silica is given bond by the addition of an organic substance, which 
produces a firm core, capable of withstanding high temperatures and 
resisting the penetrating action of fluid metal. Such a core is friable 
in the cold casting, and is, therefore, easily removed. 

"If bond is given to silica by clayey matter alone, then the metal 
bakes the cores hard, and renders their removal difficult. 

"A hard surface imparted to the sand by ramming is fatal, as fluid 
metal will not lie on it, but a hard surface resulting from the binder 
does not necessarily represent an impervious one, and fluid metal will 
usually lie quietly on it. Heat tends to loosen a sand made hard in 
this way, instead of fusing it. 

Core Mixtures 

"There should be just enough bonding material in a core mixture to 
coat each individual grain of sand, without filling the interstices between 
the grains, and the value of the core depends greatly upon the thorough- 
ness with which the mixture is incorporated. Too much attention 
cannot be given to this feature. As a rule mechanical mixers give the 
best results. The binders in common use are 



Flour, 


Linseed oil, 


Glue, 


Rosin, 


Molasses, 


Rosin oil. 



In addition to these there are many commercial binders of more or 
less value, all of them designed to offer a binder cheaper than those 
above mentioned. 

Cores made with flour, glue or molasses soften quickly when exposed 
to dampness. Therefore they must be kept in a dry place, or used soon 
after they are made. The moulds in which they are placed should be 



Dry Binders 481 

poured shortly after the cores are set. If allowed to stand for a period 
of 24 hours, the cores should be taken out and dried. 

Cores made with glue are very friable when hot and must be handled 
with great care. Less gas is given off by them than by those made 
with any other binder. Glue cores leave a smoother hole and do not 
require to be blackened as do flour cores. 

Flour is mixed with sand in proportions varying from i to 18, to i to 
30, depending upon the strain which the core is to resist. The weaker 
the mixture, the more readily the gas escapes. 

Glue is first soaked in warm water and then boiled untU entirely dis- 
solved. Glue water should consist of 2 pounds of glue to 3 gallons of 
water. This mixture is sufficient to treat 100 pounds sand. 

Rosin must be first pulverized; it is then mixed with sand in propor- 
tions of I to 20, or I- to 30, as required. 

Rosin oil is used i to 18, or i to 24 as the requirements of the case 
indicate. 

Molasses, mixed i to 20 water is used more for spraying cores to give 
a hard surface, than for entire mixtures. 

Linseed oil with sharp sand, mixed about i to 30 furnishes the best core 
of all binders. It is strong, porous and is easily removed from the 
casting. For light, delicate cores, such as gas engine and automobile 
work it is unequaled. 

Large percentages of old cores, gangway sand and moulding sand may 
be used in the core mixtures. 

Core sand should be quite damp for use, but not so wet as to adhere 
to the core box. Wet sands require much less binder than dry. 

A saving may be made in the use of flour by boiling it thoroughly 
and then using the paste (very thin) to wet the sand. As already 
mentioned, the more thoroughly the binder is incorporated with the 
sand, the better will be the cores. 

Mr. A. M. Loudon made an extensive series of experiments to deter- 
mine the comparative values of various core binders, and published the 
results in a most interesting paper presented to the American Foundry- 
men's Association at the Cleveland meeting 1906. From it the follow- 
ing extensive extracts are made. 

Dry Binders 

Test No. I. — Flour sand core mixture. _ 

Parts 

New moulding sand 2 

New fire sand i 

Flour I to 12 and i to 18 

Wet down with thick clay wash. 



482 Moulding Sand 

Cores from this mixture are usually very strong. If not thoroughly 
dried or if slightly burned or scorched, cause great trouble by blowing 
or scabbing. Cores were removed from castings with difficulty. Be- 
came damp in mould quickly, especially small cores. 

Test No. 2. — Syracuse dry core compound mixture. 

Old flour sand H 

New moulding H 

Sharp or beach H 

One part binder to 35 parts sand thoroughly tempered with water. 
Cores made from this mixture dried quickly, were clean and sharp and 
left good surface on castings. Resisted dampness well. 

Mr. Loudon states that the dampness test for each mixture was to 
dip a core partly in water, allowing it to stand after removal from the 
water for two or three days to air dry only. Iron was then cast in an 
open mould around the end which had been immersed. 

Test No. 2. — Included the water test as did all the other tests for 
dry and oil binders, the conditions being the same for all. 

The binder used in Test No. 2 stood the water test in a manner en- 
tirely satisfactory. The hot iron came in contact with the core without 
any distiubance. 

This binder in Mr. Loudon's judgment is best suited to large plain 
work, or small round and square cores. 

Test No. 3. — Dextrin or British gum mixture. 

Per cent 

Old flour sand 50 

New moulding sand - . . 25 

Beach or sharp sand 25 

I part binder to 150 parts sand, tempered with water. 

This mixture was valuable for large cores, strong, with sharp edges 
and easily dried. 

If the cores are burned in the oven, wash with some of the binder 
dissolved in water, and dry in oven for ten minutes. They are thus 
completely restored. For small intricate cores the following mixture 
was used. 

Per cent 

Old sand 33 

New moulding sand , 33 

Sharp sand 33 

I part dextrin to 100 parts sand. 

A core from this mixture was treated by the water test, and allowed 
to stand for two days. It resisted the action of melted iron better than 
cores from many mixtures, when fresh from the oven. 



Dry Binders 483 

Test No. 4. — Wago core-compound mixture. 

Per cent 

Old sand 33 

New moulding sand 33 

Sharp sand 33 

I part Wago to 30 parts sand. 

Made a good core; did not gum the box, and gave off very little 
smoke. 
A second mixture made from Wago: 

Per cent 

New moulding sand 50 

Sharp sand 50 

I part Wago to 35 parts sand. 

Unusually strong, true and sharp, but not as easily removed from 
casting as the first mixture with Wago. 

One of these cores was dipped in water and left for two days to air 
dry. The melted iron was perfectly quiet when poured around it. 

Test No. 5. — Cleveland core-compound mixture. 

Per cent 

Old sand ^^ 

Sharp sand 33 

New moulding sand 33 

I part binder to 30 parts sand tempered with warer. 

Strong core, easily removed from casting, very satisfactory for general 
use. 

A mixture i part binder to 40 sand was tried, but cores were too soft. 
Cores from the i to 30 mixture when submitted to the water test gave 
excellent results. 

Test No. 6. — Peerless core-compound mixture. 

Per cent 

Old sand 33 

Sharp sand S3 

New moulding 33 

I part binder to 30 parts sand. 

The mixture as above given was unsatisfactory, therefore, the follow- 
ing mixture was tried. 

I part binder to 20 parts sand. 

This was satisfactory, being strong and true to box, but harder to 
remove from castings than most of those previously tested. It gave 
good results when submitted to the water test. The iron showed no 
signs of blowing. 



484 Moulding Sand 

Tests Nos. 7, 8, 9 were made from samples of flour submitted. Sand 
mixed in same proportions as before. 

Thus, the first sample of flour was mixed with 15 sand, 
the second sample of flour was mixed with 18 sand, 
the third sample of flour was mixed with 20 sand. 

These were made as comparative tests of the different samples of 
flour. 

1. Made the strongest core, but was the most difi&cult to remove from 
the casting. 

2. Good for general work. 

3. Was too soft. 

A mixture of i to 18 from 3 to 9 was good, better than Nos. 2 to 8 in 
same proportion. Each of the above mixtures was subjected to water 
test and failed. When withdrawn from the water and held in hori- 
zontal position, they broke at the line of submersion. Nos. 2 and 3 were 
not as good in this respect as No, i. 

The cores from the peerless compound and most of the others resisted 
the water so that it could be wiped off with a rag without injuring the 
cores. 

Test No. 10. — Paxton dry compound mixture. 

Per cent 

Sharp sand ^^ 

New moulding sand 33 

Old sand 33 

I part compound to 30 parts sand, made a very soft core. 

When mixed i to 20 it made a very strong core. 

One of these when subjected to the water test went to pieces, while 
the last mixture made a strong open core. It is readily affected by 
moisture. 

Liquid Core Binders 

Test No. II. — Holland linseed mixture. 

Parts 

Sharp sand 30 

Oil I 

Made a strong core for small and medium shapes, but required vent- 
ing. A core from this mixture immersed in water for half an hour was 
returned to the oven and dried. It was then as good as any which had 
not been immersed. 

Test No. 12. — Syracuse core oil mixture. 

Parts 

Sharp sand 35 

Oil I 



Moulding Sand Mixtures 485 

Tempered with water and well mixed. These cores were excellent; 
without vents were not satisfactory. 

A core from this mixture was immersed for 15 hours, taken out and 
dried in the oven for 15 minutes. Molten iron when cast about it 
showed no disturbance. 

Tests Nos. 13, 14, 15. — Sterling oil samples from each of above were 
mixed at same time. 

Mixture p^^^ 

Sand ic 

Oil ;:.:::; i 

Nos. I and 2 of these samples showed too much oil. No. 3 was about 
right. 

Another mixture was then made. 



Parts 
Sand 4^ 

Oil :::::::; i 



Nos. I and 2 dried out quickly and made good strong cores, but when 
subjected to the water test the moisture acted quickly upon them, 
more so than on the other sand and oil mixtures. The cores were 
strong and were easily cleaned from the castings, but moulds which were 
left over night, and poured the next day blew very badly. 

Test No. 16. — Gluten or Esso mixture. p^^. ^^^^ 

New sand 33 

Sharp sand 33 

Old sand ^^^ 

Gluten I part to 30 parts sand 

Cores were so hard that the iron would not lay to them. 

One part gluten to 50 parts sand, — cores were good, sharp and 
strong. Iron somewhat disturbed. The gluten was mixed with water 
and the sand tempered with water. 

One part gluten to 70 parts sand. 

These cores were soft and did not stand the fire as well as the others. 
When subjected to water as before 

I to 30 stood very well, 

I to 50 became soft, 

I to 70 melted like sugar, 

showing that for a free core, one not inclined to blow, i to 70 took 

moisture very quickly. 

Test No. 17. — Glue melted in hot water mixture. p^^. ^^^^ 

New moulding sand 25 

Sharp sand 25 

Old sand 50 

I pound of glue to 100 pounds of sand for small cores. 
I pound of glue to 150 pounds of sand for large cores. 



486 Moulding Sand 

Lump or granulated glue, the cheaper the better. 

The glue water was made by dissolving two pounds of glue in three 
gallons of water. 

Cores from the first of the glue mixture when submitted to the water 
test absorbed water but held their shape. After redrying were as good 
as when first made. Should such cores be burned in the oven, washing 
them with a mixture of plumbago and glue water restores them. 

Mr. Loudon highly recommends the first of the above glue mixtures, 
using it for cores without vents for small port cores. 

Cores made from it can safely be used for all purposes, taking care to 
have them thoroughly dried. 

Cores for large beds have remained in the mould three and four days 
without causing trouble. 

Test No. i8. — Glucose melted with hot water mixture. „ 

Per cent 

Sharp sand 33 

New moulding sand 33 

Old sand 33 

I pound of glucose to 100 pounds of sand. 

Cores of every description were first class, easily dried, easily cleaned 
from casting, emitting no smoke. They acted like green sand cores, 
dried and gave good results in every respect. 

Parting Sand 

The particles of burned sand, having been deprived of combined mois- 
ture will not cohere. Such sand, taken from the cleaning room, is used 
to separate the parts of the moulds and is also dusted on patterns to 
prevent the moulding sand from adhering to them. 

A most excellent parting sand for intricate work is made by saturat- 
ing very fine burned sand with kerosene or crude oil, and setting fire to 
the mixture. 

Lycopodium is also used for parting in particular work, but the high 
price subjects it to adulteration. 

Facings 

When molten iron comes in contact with a sand mould it tends to 
penetrate the pores of the sand and to fuse the particles in immediate 
contact, leaving a rough surface or scale, varying in thickness from Mi 
to H of an inch, depending on the weight of the casting. 

Facing sands containing large percentages of carbonaceous material 
are used to prevent this difficulty and to leave smooth surfaces on the 
castings. The carbon of the facing is decomposed by the heat, and the 



Facings 487 

gases generated prevent the hot iron from attacking the sand. Facing 
sand which is composed of ground coal (sea coal), and sand in the pro- 
portions of from I coal to 8 sand, and i coal to 20 sand, depending upon 
the character of the work, is placed next to the pattern in a layer from 
y2 to i>2 inches in thickness. Back of this and completely filling the 
flask is the heap, or floor sand. By the continued use of facing the 
floor sand becomes black with it. 
The term facing includes 

Sea coal, Coal dust, 

Plumbago, Charcoal. 

Talc (or soapstone). 

It must adhere to the surface of the mould and cause the casting to 
peel when shaken out. 

Sea coal is a ground bituminous gas coal, free from sulphur and slate. 
It is mixed mechanically with new moulding sand in the proportion 
of I to 10, usually, and used generally on all work. For the purpose of 
obtaining smoother and brighter surfaces than result from the use of 
sea coal alone as a facing, the moulds are finished with plumbago or some 
mixture of which plumbago is the base. Plumbago is the best of all 
materials for this purpose. 

Soapstone is used largely in connection with plumbago as an adulter- 
ant, as also are coke dust and the dust of anthracite coal. 

The facing is applied to the mould either by hand, with a camel's hair 
brush, or it is mixed with molasses water and applied by a spray or with 
a brush. The latter method is usually used on dry sand moulds. 

Mr. W. G. Scott gives the analysis of Yougheogheny gas coal, from 
which the best "sea coal" facing is made as follows: 

Per cent 

Moisture i .00 Sulphur o. 33 

Volatile matter 35 • 00 Ash 5 . 60 

Fixed carbon 58.07 Specific gravity i . 28 

Cannel coal is also used as facing and analyzes as follows: 

Moisture 3 . 30 Sulphur o. 20 

Volatile matter 48 . 50 Ash 6 . 00 

Fixed carbon 42 .00 Specific gravity i . 229 

"Sulphur and ash are the two constituents of sea coal to be guarded 
against. If sulphur exceeds 0.75 the coal is inferior, and if sulphur is 
in excess of 1.5, the coal is unsuitable for facing. 

"Facing containing over 11 per cent ash ought not to be used. 

"Slack and culm are often ground and used as adulterants, but are 
readily detected by the amount of ash present. 



488 Moulding Stand 

Graphite Facing 

"Pure graphite contains about 99 per cent carbon, but this degree 
of purity is not found in the natural product. A high grade natural 
graphite contains 75 per cent carbon; inferior grades contain from 15 
to 65 per cent. 

"As the regulation method of determining carbon in facings is to 
burn off a weighed amount of sample and call the loss carbon, an un- 
scrupulous dealer may add coke or anthracite dust sufficient to raise 
the carbon content to any desired point. 

"Adulterations of this sort may be determined in several v/ays. 

"If several small beakers are filled with water and pure graphite, 
coke dust, anthracite dust, soft coal dust or charcoal are carefully 
sprinkled on the surface of the water, each in a separate glass, none of 
the powder will settle except the coke dust and some charcoals. This 
test eliminates coke dust and non-greasy charcoals. By shaking in a 
test tube H gram of the sample with 15 c.c. of acetone and allowing 
the mixture to stand 10 or 15 minutes, it will be seen that the pure 
graphite settles clear, leaving the liquid colorless. Coke imparts a 
gray to the solution and remains in suspension a long time; anthracite 
coal imparts a faint brown color and settles more rapidly; soft coal 
dust imparts a deep brown color. 

"The above tests are qualitative only. Equal parts of glacial acetic 
acid and sulphuric ether answer as well as acetone for this test." 

The following analyses from Scott of graphite, coke dust, coal and 
charcoal give a general idea as to the character of the diflFerent forms 
of carbon. 

Chemically Pure Graphite 

Per cent Per cent 

Moisture 0.02 Sulphur o . 00 

Volatile matter 0.09 Ash o. 10 

Fixed carbon 99-79 

Commercially Pure Graphite 

Per cent Per cent 

Moisture o. 15 Sulphur trace 

Volatile matter o. 79 Ash 4 . 46 

Fixed carbon 94 . 60 Specific gravity 2 . 293 

Stove-plate Graphite Facing 

Per cent Per cent 

Moisture o. 75 Sulphur. o. 20 

Volatile matter 5 . 29 Ash 37-66 

Fixed carbon 56 . 10 Specific gravity 2 .363 



Facings 



4S9 



The Composition of Ash in Above Sample 



Per cent 

.Silica 25.60 

Alumina 5.25 

Iron oxide 4 . 94 



Lime 

Magnesia o . 80 



Per cent 
1.07 



Cheap "Green Sand'^ Facing 



Moisture o. 45 

Volatile matter 5 . 75 

Fixed carbon 41 -49 

Sulphur 0.62 

Ash 51-69 

Specific gravity 2 .489 



Per cent 



Of which the ash analyzed. 

Silica 32.13 

Alumina 2.77 

Iron oxide 6 . 78 

Lime i . 64 

Magnesia 8.32 



This sample was said to contain 25 per cent soapstone. 
The following analyses are given for comparison. 
Coke Dust 



Per cent 

Moisture 0.19 

Volatile matter ...... i . 40 

Fixed carbon 86 . 8q 



Per cent 

Sulphur o . 98 

Ash. 10.54 

Specific gravity i .886 



Anthracite Coal Dust 



Constituents 


Selected 

lump, 
per cent 


Screenings, 
per cent 


Moisture 


.05 

4.40 

92.00 

.57 

2.98 

1.565 


3. SO 
8.99 

68.70 
.86 

17.95 
1.590 


Volatile matter 


Fixed carbon 


Sulphur 


Ash . 


Specific gravity ... 





Analysis of Soft Coal 



Constituents 


Selected 

lump, 
per cent 


Screenings, 
per cent 


Moisture 


1.39 

33.82 

58.68 

.96 

5.15 

1. 321 


4.44 
32.79 
37.61 

3.10 
22.06 

1.486 


Volatile matter 






Ash 







490 



Moulding Sand 
Analysis of Wood Charcoal 



Constituents 


Common 
variety, 
per cent 


Medicinal, 
per cent 


Moisture 


3.83 
26.57 
66.63 
None 
2.97 
1.362 


3.66 
33.15 

58.52 
None 
4.67 
1. 412 


Volatile matter 




Sulphur 

Ash 

Specific gravity 





Analysis of Soapstone and Talc 



Constituents 


Vermont 

soapstone, 

per cent 


French 

talc, 
per cent 


Silica 


51.20 
8.45 
5.22 
1. 17 

26.79 
7.17 


61.8s 

• 25 

2.61 

Trace 

34.52 

.77 










Water 





Mr. Scott gives the following as a test for the presence of anthracite 
coal in graphite. 

"Treat 0.5 gram of sample with 50 c.c. of strong nitric acid, boiling 
about 10 minutes. Then add 0.5 grams of pulverized potassium chlo- 
rate and boil until most of the chlorine is off. Dilute with 30 c.c. of 
cold water and filter, reserving the filtrate for examination. 

The filtrate from pure graphite treated in this manner should be 
clear and colorless unless iron is present, in which case it may be some- 
what yellow in color. 

The filtrate from any kind of coal and charcoal will have a distinct 
amber brown color, the soft coals giving a deeper color than the hard 
coals or charcoal. 

To confirm the test add 30 c.c. of stannous chloride solution and 
note the change in color. The graphite filtrate will be reduced to a 
colorless liquid if iron is present, or remain unchanged if free from 
iron; whereas the filtrate from the coal having an amber color will be 
much deeper in color and in some cases nearly black. The only caution 
to be observed in this test is sufi5cient boiling to remove all of the hydro- 
carbon coloring matter in the coal. 

The determination of magnesia is the only method to be rehed upon 
for detecting the addition of soapstone to graphite. Mixed with graph- 



Facings 401 

ite or anthracite dust, it answers very well for certain classes of work. 

Facing made entirely of anthracite or mixed with a low grade of 
natural graphite is termed Mineral Facing and is represented by one 
or more letters X to designate the fineness. Such facings may be added 
to wet blacking; or mixed with graphite, may be used on heavy work. 

All facings should be kept in a dry place as they readily absorb mois- 
ture. A high grade of plumbago makes the most suitable facing for 
producing bright clean castings. A good plumbago must not only 
have the proper chemical analysis, be of such refractory nature as to 
withstand the hot iron from cutting into the mould, but must also be of 
such a nature as will not retard the flow of the molten metal." 



CHAPTER XXI 

THE CORE ROOM AND APPURTENANCES 

The important relation which the core room bears to the foundry- 
product demands the most careful consideration as to location, con- 
struction and equipment. Unfortunately for the core maker, such con- 
siderations have been neglected in many foundries. Whatever could, 
has been made to serve so long as the imperative demands were 
satisfied. Good castings cannot be made without good cores. Their 
production requires the same attention and forethought as the making 
of good moulds. 

Constant intercornmunication between the moulding floors and core 
room, the handling of sand, fuel and ashes, etc., point to a location 
affording the greatest accessibility to the moulding floors and to the 
storage for sand and fuel. 

The core room should be well lighted and ventilated. The space 
allotted should be ample, not only for the convenience of the workmen 
but for storage of supplies, movable equipment, core plates, etc., so that 
the place may be kept neat and orderly. The arrangement of the 
work benches, machinery, cranes, racks, etc., must be governed by 
circumstances. 

The oven is the important feature in the core room. Where the cores 
are not very large and the demand for them not very great, some form 
of portable oven may answer the purpose. Many varieties are made, 
adapted to small and medium work. The convenience offered by them 
in placing and removing cores before and after baking, the small floor 
space occupied and the small fuel consumption commend them for 
light work. Most large foundries have one or more of these ovens. 
Where great quantities of small cores are required, some form of con- 
tinuous oven is frequently used. An oven with a revolving reel is very 
desirable for medium-sized work. 

The sketch below is taken from West's "American Foundry Practice," 
page 133. 

"The oven is round, with an upright cast-iron shaft, having five 
flanges on which to bolt plates or arms XX, the shape of which is 
shown at B. This oven is built with an 8-inch brick wall to form the 
outside and a cast-iron plate for the top, on which plate is a box D, to 

492 



The Core Room and Appurtenances 



493 



which a cap can be bolted to hold the top of the shaft, the bottom of 
which rests in a cast iron seat. 

"The fireplace should be outside of the circle, as shown, so that the 
cores will not get the direct heat from the fire. In building the walls, 
hinges HH, should be built in for hanging the oven door. 




Fig. 134. 

"This door should be made in two pieces, so as to open to the right 
and left, and should be the full height of oven, to provide for putting 
cores on the top shelves. 

"The chimney should have a top flue, as well as a bottom one, as 
shown at PP and dampers in both, so as to throw the heat down or 
up, as required. 

"When starting a fire, both dampers should be open, and when the 
cores to be dried are on the top shelf, the bottom damper may be closed, 
and vice versa. 

"This style of oven is very handy for drying cores that can be lifted 
by hand, and will hold and dry more cores with less fuel than any oven 
I know of. Should you want to dry a single core quick, put jt on the 
top shelf and turn it round to the fire. 

"This oven can be filled with cores and they can be taken out again 
without going farther than the door, which alone is of great value to 
the core maker. 

"The size of this oven was about 8 feet in diameter and 7 feet high." 
The oven was heated with a cast-iron fire basket. 

On page 135 of same book is shown a sketch for a small oven of which 
Mr. West speaks very highly. The advisability of building such an 
oven is somewhat doubtful, however, in view of the great variety of 
portable ovens on the market which can be purchased at a reasonable 
price. 



494 



The Core Room and Appurtenances 



For large cores the dimensions of the oven are governed entirely by 
the requirements of the foundry. 

Unless the drying of large moulds is comtemplated, it is not advisable 
to make an oven more than 12 feet wide by 20 feet long. Where greater 
capacity is required, it is better to duplicate it, on account of the greater 
loss of fuel in large ovens, which are not stored to their full limits. 







Fig. 135. — Core Oven. 

Among the sketches of large ovens shown by Mr. West, that on page 
227, "Moulders' Text Book," presents a most excellent design. An en- 
larged sketch is given above. The dimensions may of course be varied 
to suit the requirements. 

Mr. West in describing ovens of this design says: "They surpass 
any I know of for properly drying moulds or cores. Although we use 



The Core Room and Appurtenances 495 

slack or soft coal for the fires, a mould or core will when dry, be almost 
as clean as when first put into the oven. Another important feature 
is that the ovens will dry rapidly and still not burn a mould or core. " 

Three ovens are fired from one pit, the draft flues being at the 
extreme ends of the oven and the channel for heat to travel being di- 
verted from side to side. There is but a small chance for heat to escape 
entering through the joints and thickness of the boiler plate up into the 
oven, before it can enter the flue at F, H and K. The arrow-like lines 
represent the heat passing from the fires to the flue. The partitions X 
divert the direction of the heat and also support the covering plates 
and carriage tracks. 

The covering plates, 2, 3, 4, 5, 6 and 7 are boiler iron M inch thick, 
cut into sections the width of the flue partitions. 

The plates on the outside of the track are free at any time to be 
lifted in order to clean out the soot. Where the fire enters the first 
flue or partition,'' the boiler plates are left out, and in their place a cast- 
iron plate ¥2 inch thick, having prickers 2 inches long (on underside) 
and daubed up with fire clay is used. 

This is to prevent the direct flame from buckling and burning out the 
plates. 

There are no holes whatever in any of the plates, the heat passing 
through them and their joints, which of course are not air tight, heat 
up the oven. 

Were there holes in the plates, they would seriously injure the draught 
of the under flues, and also let much of the smoke into the ovens, thereby 
destroying essential points to be overcome in using slack for firing. 

To be able to fire with slack or soft coal, and stiH keep moulds and 
cores free from soot is something that wifl be appreciated by all moulders 
and core makers that work around ovens. Not only does soot make 
everything look dirty, but it is more or less productive of rough castings. 

"Another arrangement which I doubt being found in any other 
foundry oven is that for preventing smoke. Upon each side of the fire- 
places, about on a level with the fire, are %-\nch. openings, seen at E 
in elevation. In. the rear of these openings the brick is left open about 
4" X 6", running the entire length of the fireplace. This opening gives 
a reservoir in which the air becomes heated before being drawn into 
the fireplace. This is, I believe, claimed to be beneficial in assisting 
'smoke burning' or combustion." 

The grate surface for the fire contains an area equal to about 32''X 38". 

"The fireplaces are all faced with one thickness of fire bricks, and the 
tops of fireplaces are arched over with fire bricks. Under the large 
oven are two fireplaces. The one nearest core oven is used for heating 



496 The Core Room and Appurtenances 

the same, and is so constructed with damper arrangement, that should 
an extra heat be required in the large oven, both of the fires can be turned 
on to it. 

"As shown at D in elevation of oven, each one has a small manhole 
door, whereby the flue leading to the chimney K can be readily cleaned. 

"The tops of the ovens are covered with a series of arches. 

"Upon the tops of these ovens we store and keep shop tools, etc. The 
way the tops are formed, tons of weight can be laid upon them and do 
no harm; and the combined area of the tops makes a splendid store- 
room for systematically keeping foundry tools. " 

"Altogether the ovens are a success, and a credit to their designer, 
the late Mr. Hallo way. " 

Note. — Only one ol the ovens is shown in the sketch. The other two 
are in all respects the same as the one shown. 

Another excellent design for a large oven is shown on page 129, West's 
"American Foundry Practice." A description of one good oven is all 
that can be permitted here. 

The essential requirements for an oven are good draught and means 
for regulating it. Where the fire is made directly in the oven, as is 
frequently the case, there should be openings into the chimney at the 
top and bottom, with dampers for changing the direction and regulating 
the draught. There should also be a damper on top of the chimney 
so as to retain the heat when the fire is not urged. Aside from coal and 
coke, crude oil and natural gas are used for heating. 

The temperature of the ovens should range from 450° to 900° F. and 
must be varied somewhat according to the core sand mixtures. 

Flour sand requires a higher temperature than rosin or oil. The 
workmen soon learn the part of the oven in which the drying is most 
rapid and place the cores where they will dry quickly or slowly as re- 
quired. 

A pyrometer is a most valuable attachment and will often prevent 
the destruction of cores by overheating. 

The doors to these ovens are usually made in one piece of sheet iron 
and are provided with counter weights, so as to permit of being raised 
or lowered easily. In some cases they are made of overlapping, plain or 
corrugated strips, which are wound upon rollers. 

Core Oven Carriages 

These are mounted on wheels having anti-friction bearings. The 
top of the carriage extends over on each side as far as convenient. The 
carriages have usually three or more decks as required. The whole 



Wire Cutter 497 

is made up of bars and angles properly trussed, and left as open as 
possible, for the passage of hot air to the cores. 

The track should be evenly laid, so that there may be no jarring as 
the car passes over it. 

Mixing Machines 

Machines for this purpose are of greatest value to the core room. 
The worth of a binder and that of a core depends largely upon the 
thorough incorporation of the components of the core. Each individual 
grain of sand should receive a coating of the binding material, but the 
latter should not be present in such quantity as to fill up the pores of 
the sand. To accomplish this result requires long-continued manipu- 
lation. The best results are obtained by a mechanical mixer, driven by 
power or by hand, as the conditions permit. A machine of this sort is 
indispensable in a well-appointed core room. There are many different 
kinds on the market. The centrifugal machine is, perhaps, the most 
desirable. 

Sand Conveyors 

Many of the large foundries are provided with sand elevators and 
conveyors, whereby the sand after mixing is carried to the bench of 
each core maker and delivered through spouts. The necessity for 
appliances of this sort will be indicated by the extent and character of 
the work, simply bearing in mind that the core maker should have the 
sand delivered to him. 

Rod Straighteners 

Core wires and rods by use become crystallized, and bent in all manner 
of shapes; so that it is not unusual to find about core rooms, large 
heaps of material of this kind, which are picked over by the core maker 
in search of what he requires. In this condition it is practically worth- 
less; therefore the expense for wire and rods is not inconsiderable. By 
annealing they may be softened, and if then passed through a straight- 
ener are rendered serviceable. Both hand and power machines for 
this purpose are made. 

Wire Cutter 

A machine' for this purpose is very useful where there are many small 
cores of a kind to be made. Otherwise the common hand cutter serves 
the purpose. 



498 



The Core Room and Appurtenances 



Sand Driers 

A sand drier is frequently very desirable. A simple one can be made 
by taking a sheet-iron cylinder from, 15 to 20 inches in diameter, 
and say 5 feet long. Surround this by an inverted sheet-iron frustum 
of a cone, having a diameter at the base such that the space between 
it and the cylinder may contain any desired amount of sand. Near the 
intersection of the cone and cylinder there should be two or more small 
shding doors. Mount the cylinder on a grate for coke; provide a 
cover for the top for checking the fire. This costs little and will dry 
sand very rapidly. The cut below shows a drier in frequent use. 

The Champion Sand Dryer 

Capacity, 20 tons daily. 

Requires less fuel and has greater capacity than any of the dryers 
now in use, and being made of cast iron throughout, will outlast any 
made partially of sheet iron. 

The parts, being made interchangeable, can be 
replaced at any time. 

Set the dryer upon a solid foundation, and first 
placing casting No. i. in position, follow up with 
the other casting as numbered. 
No. I, Ash pan and base. 
" 2. Flat rings, with slides. 
" 3. Wide ring of outside casing. 
" 4. Fire box. 

" 5. Rings with which to form casing. 
" 6. Center pipe. 
" 7. Outside pipes. 
" 8. Plates to secure top of pipes. 
No. 9. Cover for pipes and seat for stove pipe. 
" 10. Flaring ring. 
" II. Slide, 
" 12. Door. 
Nos. 13 and 14. Grates. 

Fire lightly, being careful not to get the dryer too hot. Never leave 
the dryer full of sand with a fire in it; and do not attempt to use it for 
heating purposes, as it radiates no heat outside the casing. 




Fig. 136. 



Core Plates and Driers 

A great variety of core plates, varying in sizes, is required. These 
plates are usually rectangular and for sizes less than 12 X 20 are li inch 



Cranes and Hoists 499 

thick. Larger plates are thicker. Each must be smooth and true on 
one side; on the opposite side are cast stiffening strips. Larger plates 
are of sizes and shapes required. For work of extreme accuracy, the 
plates should be planed on one side. The exposure of these plates to 
frequent heating and cooling finally warps them to such an extent that 
they become unserviceable. There should- be racks for the storage of 
these plates so that any size desired may be quickly found. 

Irregular shaped cores which cannot be turned out on fiat plates, or 
which must be supported in drying, require iron shapes made to conform 
to one of the surfaces of the core. The shapes are in reality portions 
of the core boxes. The cores are baked on them, thereby retaining the 
original form when dried. 

The expense for driers is often great, therefore they should be handled 
carefully, and put away with the core boxes to which they belong. 

Core Machines 

Where great numbers of small cores of uniform cross section, round, 
square, oval, polygonal or rectangular are used, a core machine is 
of the greatest value. One of these machines will make 200 or 300 
linear feet of small core in an hour. The cores are pushed out of a 
former as sausage from a sausage machine, on to metal drying trays. 
The cores are cut up into lengths as required and pointed to fit the 
prints. 

There are several different machines of this kind made, but the 
differences are not important. 

Machines 

Moulding machines are used in making cores for plain work, where the 
demand for the product warrants. 

Machmes for making straw rope. These are little used except in 
pipe foundries. It occasionally happens in a jobbing foundry that a 
rope body for a core is required. In such a case the rope is made by 
hand. Straw rope is furnished by supply houses at low cost. 

Cranes and Hoists 

The requirements and location of these implements are regulated by 
the character of, and demand for, the work. Where the work is large 
there should be a traveling crane covering the track and the "big floor. " 
Circumstances will dictate in such cases. 



500 The Core Room and Appurtenances 

Other appliances are screw clamps, spike claws, glue heaters, clay 
tubs, horses, etc. In view of the great number of implements 
needed about a core room, the necessity for adequate room, that the 
place may be kept neatly, orderly, and as cleanly as possible, wiU be 
apparent; and as the production of good castings depends upon the 
character of the cores, as well as upon that of the moulds, the neglect 
to provide proper facilities for the core maker is inexcusable. 



CHAPTER XXII 
THE MOULDING ROOM 

Too much attention cannot be given, in selecting a location for a 
foundry, to the character of the ground; good drainage is a primary 
requisite. Gravelly subsoil is altogether desirable. If the natural 
features of the situation do not permit proper drainage, the surface 
should be raised by proper filling so that the floor may be at least one 
foot above the ground exterior to the foundry. Much damage often 
results from the flooding of the floor during severe storms. 

Pits of greater or less depth have frequently 'to be made in the floor 
for heavy castings, and if the ground is not well drained great expense 
may be involved in keeping the pits dry. 

In preparing the moulding floor the surface soil should be removed 
and replaced with coarse sandy loam. After this is leveled it should 
be covered with from 2 to 3 inches of moulding sand, rammed and 
leveled. 

Provide gangways of liberal width, one leading from the cupola and 
others perpendicular to it. The number and location of the gangways 
and the subdivisions of the floor are dependent on the character of the 
business. 

The main gangways, particularly the one leading out of the foundry, 
should be supplied with railroad tracks of standard gauge, connected 
to the switching; system. 

Where it will best serve the purpose, ample space should be set aside 
for the Foundry Office and Pattern Loft. In the selection of this 
space regard should be had for access to the pattern storage. If at 
one end of the shop, it may be overhead. 

The proper fighting of a foundry is a matter of the greatest impor- 
tance. The windows should be large and close together, and all light 
possible admitted through the roof. The monitor roof is generally 
adopted, but the saw tooth or weaving shed roof serves well. What- 
ever style is adopted, it should carry provisior for good ventilation. 
No investment can make larger returns than that expended in procuring 
a well lighted foundry floor. 

Lavatories and closets are located where most convenient. 

501 



S02 



The Moulding Room 



Cranes 

Unless the shop is small, or all the work light, a traveling crane is 
indispensable. The capacity and span of the ciane is governed by the 
conditions. Electric cranes are most commonly used and are probably 
the best for the purpose. The necessity for wall and post cranes will 
be indicated by the requirements of the business. Liberality in supply- 
ing cranes of lifting power in excess of the probable needs is never mis- 
placed. Occasions arise in every foundry which tax the cranes to their 
utmost capacity. Wire cables, instead of chains, for cranes are alto- 
gether preferable. Warning is always given of weakness in a cable, 
whereas a link in a chain may break at any moment. 

Abundant head room is a matter of great importance. Too fre- 
quently the inability to raise a heavy weight a few inches higher than 
the head room permits, occasions the greatest annoyance. 

. Hooks and Slings 

For the strength and dimensions of hooks, see Table, page 172. 

For chains, see Table, page 

173- 

Chains and hooks should be 
frequently annealed. They 
are liable to give way at any 
time and seldom give warning 
of weakness. There is an 
endless variety of chains and 
hooks devised by the ingen- 
uity of the moulder to meet 
exigencies which continually 
arise. Fig. 137 furnishes ex- 
amples of those in ordinary 
use. 

Hooks and Chains 

Figs. I, 2, 3, 4 and 5 show 
JI.S heavy hooks for the crane. 

No. I is the type of heavy 
hook for crane block. 

No. 2 is an imattached 
hook which is often found 
very convenient. 

Nos. 3, 3, 3 show different forms of change hooks. They are used in 
shifting a load from one crane to another. 




Lifting Beams 



503 



Nos. 4 and 5 "S. & C." hooks, made very heavy, are in frequent 
demand in connection with heavy lifting. 

No. 6 is the form of hook usually attached to slings for lifting iron 
They are made with flat or chisel points from iH to 3 inches 



flasks 
wide. 

No, 
No, 



7 is the ordinary chain hook. 

8 is a claw hook for shortening hitches and adjusting chain 
lengths. 

No. 9 represents beam slings for hoisting copes, rolling flasks, etc. 
The hooks should be flat and thin, 
so as to engage easily in the long 
Hnks A, A. There should be two 
or more of these long links in each 
chain, spaced at equal distances. 
Several pairs of these slings about 
every foundry where the lifting is 
by cranes are most convenient. 

No. 10 shows a most serviceable 
sling. It is usually fitted with grab 
hooks like No. 6. 

No. II is a rigid beam sling used 
on flasks with trunnions. There 
should be two or more pairs of 
this type of sling. Another form 
of trunnion sling is made of a large 
strap ring to which is attached a 
short chain with hook or ring for 
engaging the crane chains. 

No. 12 is the ordinary turn- 
buckle, an invaluable implement; 
of which there should be several pairs of varying strength. 




Fig. 138. 



Lifting Beams 

No. 13 shows a light forged beam, or spreader. This is most con- 
venient especially for light work. 

The usual lifting beam is made of cast iron with notches for slings. 
While such a beam is very serviceable, it is too heavy to handle for 
moderate weights and unsafe for heavy loads. 

No. 14 shows a beam made of oak reinforced with iron straps. 
Such a beam is light and may be used for moderately heavy 
loads. 



504 



The Moulding. Room 




Fig. 139 



No. 15 for heavy loads. 
The beam should be made 
of steel I beams, or chan- 
nels, and to carry any load 
to the full capacity of the 
crane. 

Where very large and 
heavy copes are to be lifted, 
the beam is frequently made 
in the form of a cross, so 
that attachment can be made 
in four or more places, dis- 
tributing the strain on the 
cope as desired. 

The following table gives 
the dimensions of I beams 
and loads they may safely 
carry. The table is calcu- 
lated for an extreme fibre 
stress of 12,000 pounds per 
square inch. 



Safe Loads for Lifting Beams 















Safe load for 




Depth of 


Weight 


Area of 




Width of 


extreme fibre 


between 
slings 


I 
beam. 


per 
foot, 


section, 
square 


Thickness 
of web 


flange, 
inches 


stress of 
12,000 poimds 


inches 


pounds 


inches 






per square 














inch, pounds 


8 


6 


16 


4-7 


.26 


3.63 


4,772 


10 


6 


16 


4.7 


.26 


3.63 


3.818 


8 


8 


22 


6.5 


.27 


4.5 


8,982 


10 


8 


22 


6.5 


.27 


4.5 


7,185 


10 


10 


33 


9.7 


.37 


5.0 


12,900 


12 


10 


33 


9.7 


.37 


5.0 


10,750 


10 


12 


40 


II. 7 


.39 


5. 50 


18,753 


12 


12 


40 


II. 7 


.39 


5. SO 


15,627 


14 


IS 


80 


23. 5 


.77 


6.41 


29,937 


16 


15 


80 


23. 5 


.77 


6.41 


26,200 


16 


20 


80 


23.5 


.60 


7.00 


36.225 


18 


20 


80 


23.5 


.60 


7.00 


32,200 


18 


24 


80 


23. 5 


.SO 


6.95 


38,136 


20 


24 


80 


23.5 


.50 


6.95 


34,323 



Binder Bars 



505 



No. 16 shows a cross with detachable arms. This is frequently used 
for large copes or rings, where the points of attachment must be dis- 
tributed equally. It does not answer for very great weights. Crosses 
with shorter arms cast in one piece are often of great service. 

The foundry supplies itself with such appliances as occasion requires. 



a a a 
a a a 



J 




'vnaai 



Fig. 140. 

Binder Bars 

Binder bars are usually made of cast iron, except for very heavy work, 
when steel beams are used. The binders are ordinarily made in open 
sand with the ends slotted for bolts. For heavy work holes are made 
in the ends instead of slots. 







- Upper Rib for Heavy Bars 










_-— — — —- . 


V 


1 1 


' — r- 








1 




^ 








<^ 















Fig. 141. 



The binders are held by bolts to similar bars under the bottom board 
of flask, or are fastened to anchors in the floor. For safe loads on steel 
I beams employed as binders, multiply the loads given in the table 
on page 504. 

Binder bars for supporting sides of flasks are of same character as 
those for holding down copes, except that they are shorter and not as 
heavy. 



5o6 



The Moulding Room 



Clamps 

There are many types of clamps on the market. Adjustable, steel 
and malleable iron, but it is extremely doubtful if anything has been 
found to take the place of the common, old fashioned, cast-iron clamp 
and wooden wedge. 

A large assortment of the sizes in ordinary use should be kept on 
hand. Where very long ones are required D wrought iron bars are 
bent to shape. It is the better practice, however, to use binders in 
place of exceedingly long clamps. 



^ 



1^ CFD 



Fig. 142. 



Fig. 143. 



Iron flasks are frequently held together by short clamps on the flanges. 



Flasks 

The wood flask has been used for ages and has served its purpose 
most admirably. Wood, however, is becoming so expensive that the 
iron or steel flask is rapidly superseding it. 

Cast-iron flasks are so durable and so easily made, that an assortment 
covering the ordinary range of work is almost indispensable. 

The ordinary wooden flask is nothing more than a plain box. For 
light work it is made of 2-inch plank, of width and other dimensions to 

suit the requirements. 

Fig. 144 shows the ordinary wood 
flask for light work; the ends are 
gained into the sides y2 inch and 
spiked. The upper part is called 
the cope and the bottom the nowel 
or drag. The depth of these parts 
depends entirely on the pattern. 

It is essential that the joint at 
"A" should be a plane surface, 
or as the workmen say, "out of 
wmd." 

^^^•^44. Each flask is provided with a 

bottom board B. This is made of boards one inch thick, nailed to 
battens. 
The limit for copes made with no support for the sand except that of 




Co^^. 



- Nowe/ drT>m0=:~ } \ 



r77///;/^/WJ}////////////W/ zm7m 




Flasks 



507 



the wood sides is about 20 X 20 depending largely upon the character 
of the moulding sand. 

For larger flask-bars, boards iH inch thick are placed crosswise 
of the cope and about 6 or 8 inches apart. The cope is also strengthened 
by rods at the end ^ running from side to side. The rods should have 
large washers under the nuts. There should be one or more rods at 
each end depending upon the depth of the cope. The lower edges of 
the bars are chamfered to sharp edges, and the edges are kept from 
¥i to I inch away from the pattern, the bars having been cut to con- 
form to the general shape of the pattern. Where the distance between 
the edges of the bars and the surface of the pattern is more than U inch, 
nails are driven slantwise into the bars so that their heads may come 
within three-quarters inch of pattern. 

The cope is coated with thick clay wash before placing it in position 
to receive the sand. The ordinary mediimi-sized wood cope is gener- 
ally made as shown in sketch below. 




M^ 



x^ 



< 



^W 



1 : — ,. -^r-3-^ 



> 



-^- 



Fig. 145. 

The short bars A, A are used where the copes are over 24 inches 
wide. 

The following table showing the thickness of plank desirable for 
flasks of different dimensions is copied from the Transactions of the 
American Foundrymen's Association. The table is based on a depth 
of 6 inches for copes and drags. For each additional depth of 6 inches, 
the thickness should be increased 25 per cent. 



5o8 



The Moulding Room 



Square flasks, 


Sides. 


Bars, 


inches 


inches 


inches 


24 and under 


ii/^ 


I 


24-36 


2 


1 1/4 


36-48 


2l/i 


1 1/2 


48-60 


3 


i^^ 


Rectangular flasks 


18x48 


2 


I 


18x60 


2 


I 


18X72 


2V^ 


I 


18x84 


2M 


I 


24X48 


2 


iH 


24X60 


2 


iH 


24X72 


2\(l 


iH 


24X84 


2V2 


iH 


36X48 


2I/2 


114 


36X60 


2V% 


i}^ . 


36X72 


2V1 


iV^ 


36X84 


2^/1 


iH 


48X48 


3 


ii/i 


48X60 


3 


ii/^ 


48X72 


3 


ii-i 


48X84 


3 


ii/i 



Bars should not be over 8 inches apart, center to center. 

Square flasks, from 24 to 36 inches square should have one row of 
short cross bars running through center of flask, connecting the long 
bars that extend from side to side. 

Sizes from 36 to 48 inches square should have at least one cast-iron 
bar, preferably two, and should also have one row of short cross bars. 

Sizes from 48 to 60 inches square should have two iron bars and two 
rows of short cross bars. 

With rectangular flasks, the statement that connecting bars are not 
needed until the flasks are 36 inches wide does not accord with the 
usual practice. Ordinarily connecting bars are used in flasks over 
18 inches wide. 

Rectangular flasks over 60 inches wide should have one cast bar 
crosswise in the center. Flasks over 48 inches wide should have two 
rows of cross bars and two cast bars at equal distances from the end of 
the flask. 

AU copes should have a H-inch bolt running from side to side at each 
end, and where the cope is longer than three feet it should have a bolt 
in the center. Where copes are over 6 feet long, the bolts should be 



Flasks 



509 



spaced every two feet apart. All bolts should have large washers at 

each end. 
Drags should also have bolts at each end, but as conditions often. 

prevent their use in the center, 

long-nosed clamps placed cross- 
wise every 18 to 24 inches and se- 
curely wedged are recommended. 
The form of flask shown above 

is that most commonly used 

when they are made of wood. 

It is a short-lived affair, being 

quickly knocked and racked out 

of shape, and soon goes to the 

cupola for kindling wood. Such 

flasks may be greatly strength- 
ened and their durability in- 
creased by bolting cast-iron angles 

in the corners or even reinforcing (CJ 

the corners with blocks of wood, 

well spiked to sides and ends. 

Without greatly increasing the 

cost a far better flask is made 

by making the ends of cast iron. 

Such flasks are in common use 

for making cylinders or other 

castings, requiring large circular cores as per following sketch. 

Flasks of similar construction 
are often used for cylinders as 
large as 20 inches diameter of 
bore. The sides of the flask 
must be made of plank from 3 
to 4 inches thick depending on 
the size. For rectangular flasks 
made of wood and iron, the con- 
struction shown below, offered 
by Mr. P. R. Ramp, is excellent. 

__ The suggestion to core the 

•^J-* trunnion, as at yl, is also valu- 

FiG. 147. able, as it greatly reduces the 

chance of unsoundness at that point. 
Flasks that are heavy enough to require trunnions should have iron 

ends. The trunnions may be cast on the ends or on trunnion plates, 

which are bolted to the ends. 




Fig. 146. 




Sio 



The Moulding Room 



Iron Flasks 

Although the first cost is somewhat greater, iron flasks soon pay for 
themselves by durability. They are stronger, more rigid and reduce 
the liabihty to swells and rim-outs. 

The copes and drags of small iron flasks are usually made each in 
one piece. At the joints for flasks with straight sides, flanges extend 
all the way around the inside. 

The handles may be of wrought iron cast in place, or, of cast iron, for 
sizes requiring two men to lift the cope. 

Some are made with sides turned 
up edgewise like troughs, so that the 
greatest length and breadth will be 
at the middle of the section. 

These are more expensive to mould 
and present no advantages over 
the flask with flat sides as shown 
in fig. 148. 





Fig. 148. 



Fig. 149. 



An assortment of small flasks of this description, ranging from 12 X 14 
to 16 X 18 is of great value to any foundry. 

Iron flasks of medium and large sizes are best made in sections and 
bolted together. 

Flasks of this style are made and fitted up very quickly. A few 
patterns answer for a large assortment. With proper stop-offs, the ends 
and sides can be lengthened or shortened as desired. 

Where the copes are too large to be lifted off by hand, bosses are 
cast on the end. These are drilled to receive a yoke and the cope may 
then be lifted by crane and turned. 

If the flask is heavier than can be safely lifted with such a yoke, 
trunnions may be made on the ends and heavier lifting gear employed. 

The requirements for heavy flasks are so varied that it is impossible 
to specify any general type. 

By making them in standard sections as much as possible, having 



Iron Flasks 



511 



the parts interchangeable, a rectangular flask of almost any required 
dimensions may be constructed. By so doing the number of flasks is 
greatly reduced. 




O QO 0|P 0|5| O 

O I O O 

o,ix, p o o| o o 13 ,jif> 



)'xr'o o 

o 
) o o 



Section A-B 



^ 


V 2 y^ 




)~ 1™ 




^ — ' 

a, 1 


l<^ 


^ 6 M 



Fig. 150. 

Care must be taken to number and store the parts systematically so 
that they may be readily accessible. 

It is seldom that a large flask will need to be less than 6 feet by 8 feet, 
and 12 inches deep. Starting with the end pieces 6 feet X i foot, and 
having four distance pieces, each i, 2, 3 and 4 feet long, ends can be 
assembled 6, 8, 10, 12, 14, 16 and 18 feet long; by duplicating the parts, 
the depth of cope or drag can be made any number of even feet. 

Where the depth of cope or drag is over one foot, it is desirable to 
break joints in lapping the sections. 

It is better to have the trunnion plates loose, so that they may be 
bolted to any of the 4 or 6 feet lengths. 



^ 



^ 









\m.t 



Jo o C 
3 O C 



Fig. 151. 

The top and bottom edges must be planed and the holes in ends and 
sides drilled to templets. 

Flanges top and bottom must be from 3^^ to 4 inches wide, and the 
4 and 6 feet sections drilled at the center of flanges for pins. The 



512 



The Moulding Room 



planed surface need only be H inch wide; the flanges should drop away 
from edges from H to Vie inch. 

The web of sections should be ^/i inch thick and the 
flanges iH inches. 

The Hfting is in most cases done by attaching to 
the flanges, but where the weight is too great to be 
safely borne by these flanges, heavy wrought-iron 
loops are bolted to the sections, for points of attach- 
ment. 

On page 98, "American Foundry Practice," Mr. 
West shows an admirable form of extension flask for 
moderate sizes. 

"The handles W, W, are of wrought iron cast into 
the flask. They are placed on a slant so as to be in line with the chains 
when lifting. Guides X, X should be cast on for driving stakes along 
the side. The plate Y forms the end of flask. Should it be desired to 
make the flask longer, distance pieces may be bolted in between the 
flask proper and the plate Y. 




Fig. 152. 





^ 1 i 


i 


\\\ 






.^-^^ S-^ 




vf-^ri) 








r 1 


i. 




1 1 




1 






I i 


y 


1 


€ 




1 1 


1 


1 




Q 


I 




im 


D 


ol loM 

1 j il Y 
1 'OU 




|o 



Fig. 153. 

"To accomplish the same purpose, the whole flask may be c^st in one 
piece, and the bottom edge of Y cut out H of an inch so there may 
be no bearing on the joints. When a longer flask is wanted a section 
may be bolted to it. This is not as desirable as the form shown in 
sketch." 

Flasks of this style are commonly used as copes to cover bedded work. 



Iron Flasks 



513 



Where the conditions do not warrant the extension flask as above 
described special flasks are more or less in demand. 



30 
:; 
Jo 


000 


000 


000 


000 


000 


000 


000 


000 


or 

oL 


Jo 

-.00 

-!o 


000 


000 


000 


000 


000 


000 


000 


000 


oC 

p 
ol- 


Jo 

T 

Jo 


1 


1 


000 


000 


000 


000 


000 



000 


io or 

00^ 

j oL 



Fig. 154. 

The above sketch represents an ordinary heavy flask (cope) say 
6' X 12' X 3'. 

In making large door frames, where the interior of the flask is not 
used, or for similar work, it is customary to have the flask follow the 
outline of the pattern and leave the interior vacant as shown in sketch 
below. 





; ] 


1 






-^1 








- rJ 


~^i 


!> i 








1 ( 1 


i' ^ 








I r 1 


! ^ 

ll 








r 1 


iU 

1 — r 


I J 


r-l 



Fig. 155. 

Flasks are made in all sorts of irregular shapes both in plan and eleva- 
tion, as necessitated by the patterns. The bottom plates of heavy 
flasks are made of cast iron. These are fastened to the bottom flange 
of the drag by short heavy clamps. Thus. 

Circular flasks are in common use. They 
serve as copes to wheels cast in the floor 
and for other purposes. For large wheels 
which are swept up, instead of sweeping out 
the face in a pit, large rings are used for the 
cheek. The arms and hub are made with ^^^' ^5^" 

cores and interior of wheel swept up and not disturbed subsequently. 




514 



The Moulding Room 



The cheek is rammed up against segments, and when lifted gives free 
access to all parts for finishing. 




Fig. 157, 

For wheels 16 to 18 feet in diameter the cheeks are cormnonly made 
in six segments, which are bolted together. 





Fig. 158, 

Flasks made of sheet steel pressed to shape are light and convenient. 

They are, however, much 
more expensive. They are 
not as durable as cast-iron 
flasks, and when worn out 
are of no value; whereas 
with the cast flasks, noth- 
ing is lost but the labor. 
The cuts following from a 
manufacturer's catalogue 
show standard types of 
Ught and heavy flasks. 



I 




• 






» 



Fig. 159. 



Sterling Steel Flasks 



515 



Sterling Steel Flasks 

The scarcity and increased cost of good flask lumber is making it 
necessary for foundrymen to consider other flasks than wooden ones. 

The line of steel flasks shown herewith combine strength, durability, 
lightness and efficiency. They will give splendid service. They have 
in many instances entirely supplanted wooden flasks, to the advantage 
of the user in every instance. 



Style "A" Square Ribbed Tight Flask 

Sheet Steel with Malleable Trimmings 

Stock Sizes 

Height cope and drag, 23-^2, 3, 3H, 4, 4H 
and 5 inches. 

Length cope and drag, 12, 14, 16 and 18 
inches. 

Width cope and drag, 12, 14 and 16 
inches. 

Weight less than one-half as much as cast 
flasks and practically indestructible. 

A complete small square-ribbed steel flask for general work in all 
foundries, made in above standard sizes, from which innumerable 
combinations can be made. 

Can be made in special sizes when it is required and a sufficient num- 
ber ordered to warrant the extra work in manufacturing. 




Fig. 160. 



Style "B" Round Ribbed Tight Flask 

Sheet Steel with Malleable Trimmings 

Stock Sizes 

Height cope or drag, 2)'^, 3, 3H, 4, 4^, 
and 5 inches. 

Diameter, 12, 14, 16, and 18 inches. 
From the above dimensions many com- 
binations can be made. 

The illustration gives a clear idea of 
round-ribbed steel flask for general cir- 
cular work, when the snap flask is not 
desirable. 

Weighs less than half as much as a cast flask, and is unbreakable. 




Fig. 161. 



5i6 



The Moulding Room 



Style "C" Square Con\'ex Tight Flask 
Sheet Steel with Malleable Trimmings 
Stock Sizes 

Height cope or drag, 2^^, 3, 3^, 4, 4^ 
and 5 inches. 

Length cope or drag, 12, 14, 16 and 
18 inches. 

Width cope or drag, 12, 14 and 16 
inches. 

Fig. 162. Made in the above stock sizes, which 

admit of comitless combinations of sizes. 

This flask is particularly adapted to brass, bronze, or any special 
metal foundry work. It is a new departure, having convex sides and ends 
for holding the sand. It does nice work, and while not half as heavy 
as the cast flask, is much more durable. 




Style "F" Channel Iron Floor Flask 




Fig. 163.. 
Stock Sizes 



Size, 
inches 


Depth, 
inches 


Cope, 
inches 


Drag, 
inches 


Price 


20x24 
20x28 
24x30 
24x36 
30X36 
30X42 


10 
10 
12 
12 
14 
.4 


5 

I 

6 
7 
7 


S 
S 
6 
6 

7 
7 

















Snap Flasks 



S17 



This is a decided departure in flask manufacture. It is constructed 
of structural channel steel with flanges to the outside, having a smooth 
wall on the inside. The interior is provided with staples arranged at 
intervals to permit of inserting corrugated swivel gaggers for sand 
supports. 

This type of flask does away with the flask maker entirely, as each 
moulder arranges his gaggers or sand supports to suit the necessity. 

An equipment of these flasks is an excellent investment, 

1. They cut out the use of expensive material (lumber). 

2. They practically do away with the flask maker. 

3. They eliminate expense of handling flasks. 

4. They will remain in foundry and save storage. 

5. And the most important feature to be considered is the increased 
output, better castings', less scrap, all of which will appeal directly to 
the proprietor. 

These floor flasks are furnished with a complete equipment of corru- 
gated swivel gaggers for sand supports which the moulder arranges 
easily to suit requirements. 

Snap Flasks 

Snap flasks are used by bench molders for light work. They must 
be easily and quickly handled, although snaps are sometimes made so 
large as to require two men. The flask is removed from the mould, hence 
one flask serves for an entire floor. 




They are usually made of cherry or mahogany; the hinges should 
lock and unlock quickly and be rigid when locked. The corners are 
Strengthened with iron corner bands, and the cope is faced on top with 



5i8 



The Moulding Room 



iron. For special work the joint may be made to conform with the 
parting. Rectangular snap flasks 3 feet long by 14 to 16 inches wide 
are not uncommon. For some classes of work round snaps are required. 

In the hands of a rapid, skillful moulder the snap flask is an indispen- 
sable implement for a foundry having large quantities of small work. 

Pieces weighing as much as 100 pounds may be made in the snap 
flask. 

The cuts herewith illustrate the construction of the different kinds 
of snaps referred to. 

Snap flasks of standard dimensions from i2Xi2toi2X2o can be 
purchased of most of the foundry supply houses. 

Where many moulds are to be made from one pattern, a match board, 
on which the patterns are placed, and upon which the parting is made, 
is practically a necessity. If these matches are not to be preserved, 
and are only to be used for a moderate number of moulds, they are made 
of moulding sand and fine sharp sand, half and half, stiffened with molasses 
water, or linseed oil, and dried; but if a permanent match board is desired, 
a mixture composed of one-half new moulding sand, one-half parting 
sand, >4o litharge, mixed with linseed oil and tKoroughly dried will serve 
admirably. The match should be varnished with shellac and kept with 
the pattern. Such a match board is shown in Fig. 165.. 





Fig. 165. 



Fig. 166. 



The moulds made in snap flasks must be covered with weights before 
they are poured. The weight should be about iH inches thick and 
should cover the cope entirely. 

Where the contents of the flask are quite heavy, or where the patterns 
approach the sides of the flask closely, the moulds require to be sup- 
ported by boxes, as well as to be weighted. For this purpose wood 
boxes of i-inch lumber are made so that the interior shaU have the 
same dimensions as the interior of the whole flask (cope and drag); 
this is shoved down over the mould and supports it against lateral 
pressure. Care must be taken that the boxes are not so small as to 
shave the mould nor so large as not to support it; they should just fit all 
around. 

These boxes are sometimes made of cast iron. Very serviceable ones 
made of sheet iron can be purchased at moderate prices. 



Pins, Plates and Hinges 



519 



Galvanized Iron Slip Boxes 
Straight Taper 




Fig. 167. 

The above are undoubtedly the best slip boxes on the market. They 
are more durable than wood or cast-iron boxes, are lighter and will not 
break by falling. They are made either straight or tapered, of No, 23 
iron with a No. 9 wire in top and bottom and creased. 

In ordering, state whether straight or tapered and give the exact 
size of inside of flasks. 

These boxes are for light handling and will not stand careless run-outs, 
as the hot iron will warp them. They are very rigid, however, and with 
the ordinary one-inch margin outside of pattern there will be no run- 
outs. 

When ordering taper jackets, give taper or degree per foot on side, or 
make sketch giving size of top and bottom, also depth of drag. 



Pins, Plates and Hinges 

In order that the cope of a flask, when lifted from the drag after 
ramming, may be returned exactly to its original position, so that the 
two parts of the mould may match perfectly, guides must be provided 
which will insure correct closing. 

These are frequently made of 
wood, and if kept in good shape, 
serve the purpose admirably. 
Wooden guides are especially 
advantageous for long lifts. 

Fig. 168 shows a wood guide, 
of which there should be at 
least three on the flask. The 
moulder must exercise care when 
preparing to ram up a flask, to 
see that the guides and pins are securely nailed, that there is no lateral 
play and that the cope may be lifted and returned to its place with- 
out sticking at the pins. 

Guides of this kind, while chiefly in use on wood, are sometimes 
employed on large iron flasks. In the latter case wooden blocks are 




Fig. 168. 



520 



The Moulding Room 



securely fastened in the pockets between flanges, and the guides nailed 
to the blocks. 

The usual guide for the ordinary wood flask is a common cast-iron 
plate and pin. 

These are continually getting loose and 
furnish no end of trouble to the moulder 




Fig. 170. 

as well as causing many castings to be scrapped. It is the most worth- 
less appliance of its kind. 
A very good iron guide may be made as per sketch. (Fig. 170.) 





m 



(S);^, 



^ 



HEAVY HIMOE 
Fig. 171. 



Such a guide may be fastened 
rri to the flask with very little 
more work, and the flanges give 
good support. An excellent 
pin and guide is made tri- 
angular in shape. 

Cast-iron flasks either have 

lugs to receive the pins and 

holes, or where the flanges are 

wide, pin holes are put in 

- — * them. 

Fig. 172. -Light Hinges. pj^^ ^^^ .^^^ ^^^^^ ^^^^^^ 

be accurately turned, the sizes should be standard, and those of each 



-^ m 



Pins, Plates and Hinges 



521 



size interchangeable. An assortment of such pins should always be 
kept on hand. 




Fig. 173. — Ball and Socket Hinge. 





E 



i2!h 







Fig. 174. — Heavy Hinge. 



Standard Iron Flask Pin No. 2 
For Iron Flasks 



Fig. 175. 

This is a nicely turned pin, with thread chased and hexagon nut, 
designed especially for cast-iron flasks. 



522 



The Moulding Room 
Sweeps 




Fig. 176. 

The above sketch shows the ordinary sweep used for making large 
pulleys, fly wheels, etc. A large class of work, circular in horizontal 
section, can be made with the sweep, thereby saving largely in the 
expense for patterns. 

To obtain accurate work by the use of the sweep, the stepping A 
must be firmly placed, so that the axis of the spindle B shall be vertical. 
The upper support D must be held rigidly, either by braces to wall of 
foundry or otherwise as most convenient. The box D may be made 
with a flange surrounding it from which three or four rods lead away 
to any suitable anchorages. These rods are provided with tumbuckles 
so that the spindle may be held rigidly in a vertical position. 

E is an adjustable collar fastened in position by a set screw. 

C is an iron arm carrying the wood strikes. The bearings by which 
this arm is supported should be farther apart than the width of the 
arm, so as to avoid any sagging of the latter. 

If these bearings are split in a direction parallel to the spindle and 
drawn up with clamp screws, lost motion can be taken up at any time. 
Any play in the supports for the arm, or neglect to maintain the spindle 
in a vertical position, will result in a distorted casting. Sweeps are 



Anchors, Gaggers and Soldiers 



523 



often constructed with elaborate mechanical attachments for making 
gears, spiral wheels, spiral cones, etc. 

Sometimes the steppings are placed permanently on concrete piers, 
where there are many wheels, etc., to be made. 

The strikes are cut in any desired shape and are used for inside or 
outside sweeping. Swept moulds are usually skin dried. 



Anchors » Gaggers and Soldiers 



These devices are used for sup- 
porting the sand where the ordinary 
bars are insufficient or inapplicable. 

Fig. 177 shows an anchor used 
for making pulleys. It consists 
of six cast-iron segmental plates 
about Vi inch thick, which are 
so placed between the arms of 
the puUey as to leave a space for 
sand, % inch wide, all around them. 
The upper sides of the plates are 
on the parting line of the arms. 

The plates are held together by 
wrought iron loops, passing over 
the arms, and cast in place. All 
the plates are poured at once,' and 
in open sand. 

Instead of wrought-iron loops, 



WFf] 





Fig. 177. 

these connections may be made by 
cast-iron loops, furnishing a much stiffer anchor. 
On the under side of each plate are cast one or. 
more long conical projections, which serve as 
guides by which to replace the anchor. Each 
plate is provided with an eye bolt long enough to 
reach to the joint of flask. 

The interior parting is made on center line of 
arms, sand is rammed on top of the anchor and 
another parting made flush with the rim upon 
which the cope is rammed. 

After the cope is removed, the sand covering 
the arms is lifted out by hooking to the eye bolts 
in anchor. 

Fig. 178 shows an anchor for lifting out a 



524 The Moulding Room 

Where the anchor cannot rest on the bottom, but must permit iron 
to nm under it, it is bolted to the cope and Hfted out with it. 

The necessities of the situation indicate the size and shape of anchors. 
Frequently, the pocket is such that the anchor must be broken to remove 
it from the casting. It is well to keep down the weight of the anchors 
as much as possible, relieving the cope to that extent. 

Very many cores, as well as moulds, require to be supported in this 
manner. * 

Gaggers 

In the use of gaggers it should be borne in mind, that they are heavier 
than the sand; it is simply due to the cohesion of the sand, holding 
them up to the sides of the flask or bars, that they are of assistance in 
supporting the cope. The gagger is of use just in proportion to the 
length that is surroimded with packed sand. All that part which pro- 
jects above the cope is a detriment. They are first immersed in thick 
clay wash, and placed flat up against the bars or sides of flask, having 
about % inch sand under them. They are made in the gagger mould, 
already described, which is kept near the cupola. Costing practically 
nothing, they may be used freely. A good supply should always be 
kept on hand. 

Many shops use gaggers made of Vi inch square bar iron bent to 
shape. They are not as serviceable, however, as they do not offer as 
good a surface to which the sand can adhere, and are more expensive. 

Soldiers 

Soldiers are simply pieces of wood about one inch square, cut from 
boards, with clay washed and placed around the mould instead of gag- 
gers, where the latter cannot be used; or to assist the gaggers in deep 
lifts. The sand adheres to soldiers better than to gaggers. 

The free use of either gaggers or soldiers is to be encouraged, as it 
is better to place too many of them in a mould than to have a drop. At 
the same time care must be exercised to have the ends well protected 
by sand, so that the hot iron will not come in contact with them, as 
there will surely be a "blow" in that event. 

Sprues, Risers ajid Gates 

The following tables, giving the equivalent areas of round gates, also 
of square and rectangular gates as compared with round ones, are taken 
from West's "Moulder's Text Book," pp. 245 and 246. 



Table of Equivalent Areas of Gates 



525 



Table 


or 


Equivalent Areas of 


Round Gates 




One iH inch 


is equal 


in area to two 


I 


He, three ^, 


or four %-inch gate 


" 13/4 








" 


iH 




I * 


J^ 


" 2 








<( 


l7l6 




I Me 


I 


" 2H 








a 


iH 




iMe 


iH 


" 2H 








11 


iM 




iMe 


iH 


" 2% 








(I 


I^Me 




iH 


1% 


" 3 








u 


2^^ 




1% 


iH 


" 3H 








u 


2M6 




I^i 


i5i 


" 3H 








(I 


2^^ 




2 ' 


iH 


" 3^'^ 








" 


2IH6 




2?^6 ' 


i^/i 


" 4 








(i 


2IM6 




2M6 


2 


« 4H 








a 


3 




2V16 


2H 


" 4H 








a 


3M« 




2H 


2M 


" 4H 








a 


3?^ 




2% 


23/i 


" 5 








" 


3?i6 




2% 


2^ 



Note. " The fractional parts of an inch as seen by the table are not carried out any 
further than Me, for the reason that the subject does not call for any closer figures. 
Therefore, the figures given will be understood as being ' nearly ' equal in area. 
As given, the sizes can be readily discerned, and are also applicable to measurements 
by the shop pocket rules commonly used." 



Table of Eqltvalent Areas in Square and Rectangular 
Gates to That of Round Gates 

(See note above) 



Round 


Square 
gates 


Rectangtilar 


Rectangular 


Rectangular 


Rectangular 


gates. 


gates 


gates 


gates 


gates 


inches 


I inch thick 


iH inch thick 


2 inches thick 


21-^ ins. thick 


I 


-'A 










t^ 


iMe 










m 


l9/i6 


IX 23/^ 








2 


m 


IX 3% 


ii^X 2H6 






2H 


2 

23/6 
2M6 


IX 4 
IX 5 
IX 6 


ii/iX 2IM6 
iHX 3^6 
l}iX 4 






2H 






2% 


2X3 




3 


211/16 


IX 7M6 


li/X 4% 


2X39i6 




3Vi 


2jt 


IX SMe 


li^X S/2 


2X4^6 


2^X3M6 


3H 


3H 


IX 9H 


li/iX 6^6 


2X4^i 


2^X3% 


3% 


35/6 


iXiiHe 


li/^X 7% 


2XS^/i 


2HX4H6 


4 


391 6 


IXI2?16 


iHX &% 


2X61/ 


2HX5 


m 


33/4 


1X14^6 


iHX 9H 


2X7^/^ 


2HXSH 


AVi 


4 


1X151^6 


iI^XiqS^ 


2X8 


2HX6% 


m 


4^6 


1X17% 


ii/^Xili^e 


2X87/i 


2HX7% 


5 


4^6 


1X19H 


1HX13H6 


2x913/6 


2Vixm 



"The term 'equivalent' used does not imply that two or more small gates having 
a combined area equal to one large gate, all having like 'head pressure,' will deliver 
the same amount of metal per second." 



526 



The Moulding Room 



"The flow of metal is retarded by friction in proportion to the surface 
area with which it comes in contact. Now although four 2V^-inch round 
gates are of equal area to one 5 -inch roimd gate, we find the frictional 
resistance to the flow of a like 'head pressure' through four aJ^-inch 
round gates to be double that generated in one 5-inch round gate, 
simply because the combined circumferences of four 2H-inch round gates 
are 31.416 inches, whereas the circumference of one 5-inch round gate is 
15.708 inches. As gates are generally combined under varying compli- 
cated conditions, the tables as given can be better practically used than 
where they are lumbered with the question of frictional resistance. " 
Risers are generally double the diameter of the pouring sprue. The 
function of the' riser is twofold. It 
serves to catch and carry away any 
dirt entering the mould from the pour- 
ing sprue and also to furnish a supply 
of Uquid metal to provide for shrink- 
age. Risers are placed either in con- 
nection with the gate, or on some part 
of the mould whence the deficiency 
from shrinkage can be most readily 
supplied. When located on the gate 
the latter is usually so cut as to impart 
a whirling motion to the metal ascend- 
ing the riser. The metal enters the 
riser near the bottom and flows to the mould through a channel opened 
above the entrance. 

In the sketch A represents the pouring sprue, B is the riser, C the 
gate from sprue to riser which is cut tangential to B. D is the gate 
from riser to casting. The gates should be somewhat smaller in area 
than the pouring sprue so that the pouring basin E may always be kept 
full. 

Top Pouring Gates 

The advantage of this form of gate 
for large castings is that the dirt is 
kept at the top of the poUring basin, 
allowing the clean iron to flow into 
the mould from beneath. 

The first dash of iron may carry 
some dirt, but the greater portion 
of it will flow with the stream over 
the gates; the runner being quickly 
filled, no dirt can enter subsequently if kept full. See West's "Moulder's 
Text Books," page 129. 




Fig. 179. 




Fig. 180. 



Horn Gates 



527 



Whirl Gates 

The object of the whirl gate is to impart a rotary motion to the iron 
in the basin and riser B, B. 

By centrifugal force the metal is kept in contact with the exterior 
of the riser, and the dirt is carried up in the middle of it. 





Fig. 181. 

The riser B should be larger than the pouring sprue A , and A should 
be larger than C, in order that the pouring basin may be kept full. 

It is best to have patterns made for whirl gates; they can be used in 
either cope or drag. 

The "Cross" Skim Gate 

This as shown in Fig. 182 is an excellent device and is largely 
used. 

A is the gate leading from pouring sprue to 
basin B, C is a, core in which is the gate D, 
leading to casting. The iron enters B, tangen- 
tially, a whirhng motion is imparted to it carry- 
ing the dirt to the riser, 
while the clean iron flows 
out through D. 

Another form of same gate is made as shown 
in fig. 183. 

It diflfers from the first form simply in having 
a flat core E placed acrpss the gate D, instead 



CP<J^ 




Fig. 182. 



Fig. 183. 
of forming a part of it 



Horn Gates 



These are principally used for bottom 
pouring, leading from the parting of 
flask to the casting below. 

They are made smaller at the point 
joining the casting to permit of easy 
removal and to choke the stream of metal. 




Fig. 184. 




The Moulding Room 

Pouring basins have frequently skimming 
cores placed between the basin and the down 
sprue to hold the dirt in basin. A pattern is 
usually made for them. 



Strainers and Spindles 

Fig. 185. Thin perforated plates from He to %2 inch 

thick, and wide enough to cover the entrance to pouring gate are fre- 
quently placed in the runner 
basin over the gate. When the 
iron strikes the strainer it is held 
back until the latter is melted 
allowing the basin to fill partly, 
raising the dirt to the surface 
and furnishing clean iron to the 
gate 
purpose 




Fig. 186. Spindle gate 
Spindle gates consisting of many small gates serve the same 



Weights 

For medium castings, weighting the copes will be found more con- 
venient than the use of binding bars. There should be about every 
foundry a large assortment of weights depending on the class of work. 
Weights to be handled by the crane will be found more convenient, if 
made square in cross section and of whatever length desired. Holes 
are cast in the ends into which bars are inserted for Hfting. Weights 
made in this way are more readily piled than if provided with eye bolts. 

Chaplets 

Chaplets are properly anchors, and should come under that heading. 
They are used mostly for securing cores in place in moulds. Except for 
special requirements the foundryman can procure chaplets from the 
supply houses far cheaper than he can make them. Cuts and sizes of 
the various chaplets in use are given below. 

The Peerless Perforated Chaplet 




Fig. 187, 



Liquid Pressure on Moulds 529 

Manufacturers of all classes of castings requiring small cores will 
readily observe the advantage in using a chaplet, such as is illustrated 
above. 

Made from perforated tin-plated sheet metal, insuring perfect ven- 
tilation of the chaplet, eliminating all possibilities of blow holes, air 
pockets, chills, etc., forming a perfect union with the molten metal, 
thereby insuring an absolute pressure tight joint; something not ob- 
tained with any other chaplet on thin work. Through its use, not only 
are time and labor of the workman saved in adjusting the cores to the 
matrix of the mould, particularly on water backs or fronts, radiators, gas 
burners, pipe fittings, gas and gasoline engine work, and similar castings, 
but it also greatly lessens the hability of flaws, defects and consequent 
losses in castings, such as commonly result from the ordinary chaplets 
or anchors now in use. 

Liquid Pressure on Moulds 

The pressure of the liquid metal at any point of the mould is deter- 
mined by multiplying the distance in inches from that point to the top 
of the metal in pouring basin by .26 pounds. The product is the pressure 
in pounds per square inch. 

To overcome this pressure laterally, reliance is placed on the rigidity 
of the flask, supported, if necessary, in deep castings by binding bars. 

The binding bars are of same character as those already described for 
holding down copes. They are tied across top and bottom of flask by 
rods, or otherwise. 

The static pressure on the cope is ascertained by multiplying the area 
of the casting in square inches, at the joint of the flask by the height 
in inches from the joint of the flask to level of iron in pouring basin 
and by .26 pounds. 

In addition to this there is the pressure due to resistance in overcoming 
the velocity of the rising iron, which pressure is measured by one-half 
the product of the weight of the rising iron by the square of the velocity. 
WTiile this pressure may be acciurately calculated with sufficient data, 
it is usually difficult to get them, and the results are, therefore, only 
approximate. 

However, when the mould is nearly full, the pouring is slackened as 
much as possible without letting the dirt into the sprue, thereby reduc- 
ing the head and velocity, and greatly lessening the shock as the iron 
reaches the cope. 

The formulae given for determining holding down weights for copes 
are empirical. The moulder will not be led astray by calculating the 
lifting area of the mould in square inches, multiplying this by the head 



53d 



The Moulding Room 



measured to pouring basin, in inches, and this product by .26 pounds- 
Add 20 per cent to the result, this will make ample provision for the 
lift due to the blow of the rising iron. 



The Peerless Perforated Chaplet 

The following list will give an idea of the approximate number of the 
various sized chaplets required to make a pound. 



Length 


Breadth 


Thickness 


No. to the 
pound 


% 


H 


% 


1600 


Vi 


% 


H 


1400 


Vz 


Yi 


H 


1200 


Vi 


Vi 


3/16 


IIOO 


% 


% 


3/16 


600 


I 


I 


M 


300 


% 


% 


H 


250 






H 


130 






% 


100 


iH 


iVi 


Vi 


80 






Yi 


90 


iH 


IH 


3/4 


80 






3/4 


45 


2H 




I 


35 






I 


40 


m 


1 1/4 


I 


30 



Over two thousand different shapes, sizes and styles of these chaplets 
are made. Many hundred standard sizes and shapes are kept in stock. 

The prices depend upon the sizes and number required to make a 
pound. 

The Peerless Perforated Chaplet. — {Continued) 

(Net prices per pound.) 



No. to the 


1 
Price per 


No. to the 


Price per 


pound 


pound 


pound 


pound 


20- 40 


$0.35 


200- 2SO 


S0.8S 


40- 50 


.35 


250- 300 


.90 


50- 60 


.40 


300- 3SO 


95 


60- 70 


.45 


350- 400 


1. 00 


70- 80 


.50 


400- 500 


1.05 


3o- 90 


.55 


500- 600 


1. 10 


90-100 


.60 


600- 700 


I. IS 


ioa-125 


.65 


700- 800 


1.20 


125-IS0 


.70 


800- 900 


1.25 


150-175 


.75 


900-1000 


1.30 


175-200 


.80 


lOOO-IIOO 


1. 35 



ChapletS 



531 



Double Head Chaplet Stems 

Plain or Tinned 
inch round iron, H to i H inches long (measur- 



Made of 
ing from face to shoulder). 

Price per hundred, from ^A to iH inches . 
Price per hundred, from iH to 2^4 inches. 



$4.00 
5.00 



^^p 



Fig. 188. 




Fig. 189. 



Double Head Chaplets with Forged Heads 

Plain or Tinned 

Made of %-inch round iron, from H to 2H inches long, 
with head above %-inch diameter. 

Price per hundred, from H to iH inches. . $5.00 
Price per hundred, from iJ^^ to 2H inches. 6.00 



With Square or Round Plates Fitted 

Plain or Tinned 




Fig. 190. 

Square plates always furnished unless otherwise ordered. 
Stems made of He inch round iron from ¥& to iH inches long. 

Price per hundred, % to ^A inch with plates any size $4.00 

Price per hundred, H to i inch with plates any size 4 -50 

Price per hundred, i>i to iH inch with plates any size. . . 5 .00 



Stems made from M-inch round iron from H to 2H inches long. 

Price per hundred, H to i inch with plate any size $6.00 

Price per hundred, i to iH inches with plate any size. . , " 
Price per hundred, i^^ to 2 inches with plate any size.. . . " 
Price per hundred, 2 to 2H inches with plate any size "' 



532 



The Moulding Room 



Price List of Double Head Chaplet Stems 

(Plain or tinned with square plates fitted, heavy stem and plate.) 



Diameter 
of stem 



Length 



I 

m 
2 

214 



3K2 
3% 
4 

4K 

4K2 



I 

m 
2 

2H 
2l/^ 
2% 

3 

3H 
3!/^ 
3% 
4 

4}4 

4^/4 
5 



Per 100 



$8.00 
8.00 
9.00 
10.00 
11.00 
12.00 
1300 
14.00 
15.00 
16.00 
17.00 
18.00 
19.00 
20.00 
21.00 
22.00 
23.00 
24.00 
9.00 
9.00 
10.00 
11.00 
12.00 
1300 
14.00 
15.00 
16.00 
17.00 
18.00 
19.00 
20.00 
21.00 
22.00 
23.00 
24.00 
25.00 



Diameter 
of stem 



Length 


Per 100 


^ 


$10.00 


I 


10.00 


iVi 


11.00 


1]^ 


12.00 


m 


1300 


2 


14.00 


2K 


15.00 


2H 


16.00 


2% 


17.00 


3 


18.00 


M 


19.00 


3H 


20.00 


3% 


21.00 


4 


22.00 


4H 


23.00 


4H 


24.00 


4% 


25.00 


5 


26.00 


li 


11.00 


I 


11.00 


iH 


12.00 


i>i 


1300 


1% 


14.00 


2 


1500 


2M 


16.00 


2\i 


17.00 


2% 


18.00 


3 


19.00 


3M 


20.00 


3>^ 


21.00 


3% 


22.00 


4 


23.00 


AM 


24.00 


AM 


25.00 


A% 


26.00 


5 


27.00 



Wrought-Iron Chaplet Stems 



533 



Wrought-Iron Chaplet Stems with Square or 
Round Plates Fitted 

Plain or Tinned 




Fig. 191. 

Square plates always furnished unless otherwise specified. 
Price per Hundred 



Diameter of plates . . 
Thickness of plates . 
Diameter of stem. . . 



iVi ins. 


ij^ ins. 


1% ins. 


2 ins. 


21-^ ins. 


He in. 


%4 in. 


\i ins. 


1 Mi in. 


Me in. 


Hin.- 


Me in. 


% in. 


H2 in. 


5/8 in. 


$3.10 


$5.10 


• $6.70 


$11.30 


$20.00 


3. IS 


5. IS 


6.80 


II. 4S 


20.2s 


3.20 


S.20 


6.90 


11.60 


20.50 


3.25 


5.25 


7.00 


II. 7S 


20.7s 


3.30 


5.30 


7.10 


11.90 


21.00 


3.35 


S.3S 


7.20 


12. OS 


21.25 


3.40 


5.40 


7.30 


12.20 


21.50 


3.45 


S.4S 


7.40 


12. 3S 


21.75 


3.50 


5. SO 


7. SO 


12.50 


22.00 


3.55 


S.55 


7.60 


12.65 


22.25 


3.60 


5. 60 


7.70 


12.80 


22.50 


3.70 


S.70 


7.90 


13.10 


23.00 


3.80 


5.80 


8.10 


13.40 


23.50 


3.90 


S.90 


8.30 


13.70 


24.00 


4.00 
\ 


6.00 


8. so 


14.00 


24.50 


1 - 


• SO 


.60 


.75 


.90 



3 ins. 
Yi in. 

Vi in. 



Length, inches 
3 

zY^ 

4 

aM 

5 

SH 

6 

m 

7 

7^ 

8 

9 

10 

11 

12 

Net prices for curv- 
ing plates to suit 
diameter of core 



$31.25 
31.62 
32.00 
32.37 
32.75 
33.12 
33.50 
33.87 
34-25 
34.62 
35. 00 
35.75 
36.50 
37.25 
38.00 

1. 25 



534 



The Moulding Room 



Wrought-Iron Chaplet Stems 

Plain or Tinned 



\sfYmv 



Fig. 192. 
Price per Hundred 



Length, 
measuring from 


Diameter 


face to stem, 
inches 


H 


5/16 


% 


1/^ 


% 


% 


3 


$2.40 

2.45 
2. so 
2.55 
2.60 
2.65 
2.70 
2.7s 
2.80 
2.85 
2.90 
2.95 
300 
3 OS 
3.10 


$3 fi=: 


S4.50 
4.60 
4.70 
4.80 
4.90 
5.00 
5.10 
5.20 
5.30 
5.40 
5.50 
5.70 
5. 90 
6.10 
6.30 


% 8.2=; 


$13.00 
13.25 
13.50 
13.75 
14.00 
14.25 
14.50 
14.75 
1500 
15.25 
15.50 
16.00 
16.50 
17.00 
17.50 


$19.20 


31^ 


3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
4 


70 
75 
80 
85 
90 
95 
00 
05 
10 
20 

25 

30 

35 


8 
8 
8 
8 
9 
9 
9 
9 
9 
9 
10 
10 
10 


40 
55 
70 
85 
00 
15 
30 
45 
60 
85 
20 
55 
90 
2=; 


19.60 


4 • • 


20.00 


aH . 


20.35 


5 


20.85 


S^i 


21.20 


6 


21.60 


6H 


21.95 


7 


22.30 


71^ 


22.65 


8 


23.00 


9 


23.75 


10 


24.50 


II 


25.25 


12 














Gray Iron Chaplets 



Fig. 193. 

Length, inches. . . H % Vi % H % i 

Per hundred ... . $0.72 $0.78 $0.84 $0.90 $1.00 $1.10 $1.20 

Length, inches. . . xM iH iH i^^ iH 2 

Per hundred $1.40 $1.60 $1.70 $1.80 $2.20 $3.00 

Double Head Water Back Chaplets 

Made of ^ie-inch round iron, from H to 2H inches long, 
with heads about % inch in diameter. 

Price per hundred, from H to iH inches. ... $5.00 
Price per hundred, from iVz to 2>^ inches. . . 6.00 



Fig. 194. 



Radiator Chaplets 



535 



Wrought-Iron Chaplets with Forged Heads 

Plain or Tinned 




Fig. 195. , 
Price per Hundred 



Diameter of head. . . 


1/^,1 He 
and 1^6 


i}i 


iH 


m 


iH 


2 


Diameter of stem. . . 


and Vi 


Vie 


H 


V2 


H 


H 


Length, inches 
3 


?2.40 

2.45 
2.50 
2.55 
2.60 
2.6s 
2.70 
2.75 
2.80 
2.85 
2.90 
2.95 
3.00 
3.0s 
3.10 

.40 


$3.6^ 


$4.50 
4.60 
4.70 
4.80 
4.90 

5-00 
5.10 
5.20 
5.30 
S.40 
5.50 
5.70 
5.90 
6.X0 
6.30 

.75 


$ 8.25 
8.40 
8.55 
8.70 

8.8s 
9.00 
915 
930 
9-45 
9.60 
9.85 
10.20 
10.55 
10.90 
11.25 

1. 00 


$13.00 
13.2s 
13.50 
13.75 
14.00 
14.2s 
14.50 
14.75 

IS. 00 

15.25 
15.50 
16.00 
16.50 
17.00 
17.50 

1.25 


$19.20 
19.60 


3H 


3 
3 
3 
3 
3 
3 


70 
75 
80 
85 
90 
95 
00 
05 
10 
20 
25 
30 
35 
40 

60 




4^ ••• 


20.35 
20.85 
21 20 


SH 


6 




6}^.. 


21.95 
22.30 
22.65 
23.00 
23.75 
24.50 
25.25 
26 00 


7 


7H 


8 


9 




II 


12 


Net price for point- 
ing 


1.50 











Single Head Water Back Chaplets 

Head H inch, stem Vis inch, length to order. For price /%__» 
list see Wrought-iron Chaplets with Forged Heads. x^T™'^ 

Fig. 196. 



Radiator Chaplets 

I "^ Head % X %, stem and length to order. 

LIT' 

Special chaplets and plates made to order. 
Fig. 197. 



536 



The Moulding Room 



Round and Square Head Chaplets 

Stems made of Me-inch round iron, from 5^ to iH inches 
long. 

Plates Vi inch round and % inch square, Me, %, H, %, H, H 
Fig. 198. ^^^ ^ '^^^^ ^ong. 

Price per hundred, all sizes $3 .00 




Tinned Clout Nails 



^■. 



Fig. 199. 

An indispensable article in the foundry. Do not rust like the ordinary 
black cut nail. Shipped in 100-pound kegs. All lengths from Vs inch to 
2 inches, inclusive. 

List Prices 



Inches 


1 

Per pound 


3-8 


$0.70 


31/^-8 


.60 


1-2 


.50 


4^/^-8 


.45 


5-8 


.43 


5H-8 


.41 


3-4 


.40 


6H-8 


■ 39 


7-8 


.38 


I and longer 


.36 



Pressed Tin Shell Chaplets 

For certain classes of work these chaplets are inval- 
uable. They form perfect union with the cast metal. 

Sizes H inch to H inch inclusive are made in both 
two and three prongs, ^He inch to i inch inclusive 
are three prong only. 




Fig. 200- 



Sprue Cutters 
Price List 



537 



Size, 


Two prong, 


Three prong, 


Inches 


per thousand 


per thousand 


M 


$300 


$3.50 


M 


300 


3. so 


Me 


3.20 


3.70 


% 


3.50 


4.00 


Me 


3.50 


4.00 


1/^ . 


4.00 


4.50 


9i6 


4.00 


4- SO 


% 


4. SO 


S.oo 


iHe 




S.oo 


% 




S-Oo 


1^6 




S-oo 


% 




S.25 
5.25 


1^6 




I 




S.2S 





Steel Sprue Cutters 



<S> % 



u u 



Fig. 201. 

These sprue cutters are all 6 inches in length. 
They are made of steel and in four sizes, viz. : 

No. I. — H inch at bottom, % inch at top. 

No. 2. — % inch at bottom, i inch at top. 

No. 3. — Vi inch at bottom, iM inches at top. 

No. 4. — % inch at bottom, iH inches at top. 

Price 50 cents each 



Brass Sprue Cutter 

Fig. 202. 54-inch diameter, 10 inches long. . .$4.80 per dozen 



CHAPTER XXIII 
MOULDING MACHINES 

The moulding machine has become of such importance that no f oimdry 
can afford to be without it. The reduction of cost in the production 
of the classes of work for which it is adapted and the superiority of the 
product as compared with hand work render the machine absolutely- 
indispensable to the successful conduct of a foundry engaged in com- 
petitive work. 

While the moulding machine is in some respects invaluable, it must 
not be supposed that its value can be realized without the exercise of a 
high order of intelligence. 

To produce accurate work by machine requires the utmost care and 
accuracy in fitting up patterns and flasks. Apphances which may be 
used successfully in hand moulding would entail disastrous results in 
machine moulding. Again, no particular machine is adapted to all 
kinds of work. It has a certain range for a certain character of pro- 
duction. Without those limits its use is not warranted. 

There are many kinds of machines, operated in various ways; by 
compressed air, hydraulic pressure, mechanical pressure, gravity and 
impact. 

It is not the purpose of this book to discuss the merits of the different 
machines. The various types have been in service long enough to 
indicate the particular class of work to which each is best adapted. 
One type of machine is best suited for light, small work; another to 
stove-plate; another to car castings, etc. 

In choice of machines the foundryman should profit by the experi- 
ence of those who have preceded him in this field, and must be especially 
cautious in not attempting to extend the range of any one type beyond 
that for which it is particularly fitted. 

There are machines which simply perform the operation of ramming; 
others which only draw the pattern, the ramming having been done 
by hand; while others perform both operations. In many instances 
the character of the work determines the function of the machine. 

It is doubtful, however, if hand ramming for deep pockets, etc., can 
be dispensed with by use of the machine. In fact, except in cases where 
the plainest character of work is produced, it is a mistake to believe 

538 



Moulding Machines 539 

that the moulding machine does not reqmre the services of an experienced 
moulder. 

Mr. S. H. Stupakoff, in his comprehensive paper on the moulding 
machine, referring to the object of the machine as one to save labor, to 
increase the output, to decrease cost of production, to produce uniform 
and better castings, etc., says: 

"It is obvious that it would require a complicated mechanism to per- 
form successively and successfully all the necessary operations to make 
a complete mould, even if it were only the mould of a simple pattern. 
In consequence the general equipment of a foundry which accom- 
plishes this object must be necessarily quite an elaborate and expensive 
matter. The majority of designs of moulding machines run in this 
direction, whereas in most cases it would have been better if the energy 
expended had been directed to their simplification. 

"Such tendencies lead to complications which are altogether unsuited 
for foundry practice; they meet with little favor and machines built 
upon these principles are of short Hfe." 

"Only the simpler moulding machines have a chance of meeting with 
more or less success, even if they perform but a few operations, provid- 
ing they perform these well." 

"The first step in the evolution of the moulding machine was a device 
for withdrawing patterns from the sand. The next was to employ 
stripping plates, then an attempt to ram the mould by machinery." 

In these three operations He the basic principles of all moulding ma- 
chines: all subsequent improvements and additions have been matters 
of detail; but to these improvements and to superior workmanship is due 
the real success of the modern moulding machine. 

In the chart (p. 549), given by Mr. Stupakoff, moulding machines 
are divided into two classes — hand and power machines. The chart 
gives the variations of each class. 

The selection and arrangement of machines, etc., is a matter governed 
entirely by the specific circumstances. Only hand machines are portable. 
They effect a great saving in the cost of carrying sand, but their use 
is Hmited by their size and weight. Mr. Stupakoff discusses the advan- 
tages and use of pattern plates as follows: 

"At first sight it may appear that the construction and manipulation 
of pattern plates has but little connection with moulding machines, but 
I hope that I will succeed in showing in the course of this work, that 
they are not only intimately connected with each other, but that they 
are in fact the principal parts of all moulding machines. The lack of 
intimate knowledge of how to make use of them to the best advantage, 
the want of proper means to effect this purpose and the wretchedly 



540 Moulding Machines 

little effort which is made to catch the right spirit of their nature, is 
generally the reason why a moulding machine becomes an elephant on 
the hands of the moulder and an eyesore to its owner." 

The recommendations given by Mr. Stupakoff for the adoption of 
plate moulding by hand apply equally well to machine moulding. 

1. Plated patterns give the best service when used continuously. 

2. Castings which are to be produced in quantities are perferably 
moulded with plated patterns. 

3. Standard patterns are preferably plated for economic production 
in the foundry. 

4. Plated patterns should be made .of metal to give good service." 

5. When plated patterns are used good flasks only will insure good 
castings. 

6. Accurate workmanship is one of the main requisites in plated 
patterns. 

7. The use of wood patterns on plates is not excluded. 

8. All patterns when placed on plates should be provided with 
plenty of draft. 

9. Plated metal patterns are preferably made hollow. 
10. Rapping is destructive of plates and patterns." 

The chapter on jigs is regarded of such importance that it is given 
here in full. 

The Moulding Machine 

By S. H. Stupakoff, Pittsburgh, Pa. 

Journal of the American Foundrymen's Association, Vol. XI, June, 1902, Part i. 

Jigs 

The deduction arrived at in the foregoing chapter might make it 
appear that plated patterns are not Ukely to find extensive use in 
jobbing foundries, whereas this is really not altogether the case. There 
is no doubt that plate moulding as now practiced, or rather as ordi- 
narily applied, is practically excluded from jobbing shops. But, if a 
plate is used in connection with a suitable jig, specially prepared for the 
purpose, objections are not only overcome, but the application and use 
of plates offer excellent advantages, even in such cases where only a 
small number of castings of the same pattern are required at one time. 
At best, the economic use of plated patterns is limited by the shape and 
size of the castings. The fundamental principle involved in their 
construction and application must be fully understood by the user, 
if satisfactory results are expected. 



Jigs 



541 



Irrespective of its relation to the moulding machine, it would seem that 
this subject — on its own merits — is of such importance, that it should 
be investigated by all foundrymen. It should specially interest the ma- 
jority of our members. I have therefore somewhat enlarged the scope 
of this treatise on the moulding machine by including a detailed study 
of the construction and modus operandi of this particular contrivance. 

To begin with, it should be understood that all plates are provided 
with guide-pin holes, which are accurately fitted to corresponding guide 
pins forming part of the flasks. Unless special flasks are used in con- 
nection with such plates the customary flask pins should not be con- 
foimded with these guide pins, as they will never answer the purpose. 
In order that misconceptions in this respect may be avoided, this term 
will be adhered to in what follows, and strict distinction will be made 
between flask pins and guide pins wher- 
ever they may be mentioned in the 
course of this work. 

The guide-pin holes, G and G', Fig. 
205, are preferably arranged on opposite 
ends of the plate, in even multiples of an 
inch, and equidistant from its center and 
on a line dividing the plate into two 
equal rectangles. There are exceptional 
cases, in which three or four guide pins 
must be used. The most serious objec- ^°^- 

tion against this arrangement is the greater difficulty experienced in 
locating the patterns correctly. 

Accuracy in preparing the plates becomes of the utmost importance, 
as the magnitude of all errors occurring in the original laying out is 
doubled by each subsequent operation. The guide-pin holes should be 
drilled and reamed out at right angles to the surface of the plate, and it is 
advisable to provide them with hardened and ground steel bushings. 
All guide pins should be of uniform diameter irrespective of 
the size of the plate. A pair of test pins should be kept on 
hand, which snugly fit the guide-pin holes; one-half of one of 
their ends should have been cut down to about H inch in 
length, leaving as remainder exactly one-half of the cylindrical 
portion (Fig. 204). If these test pins are inserted into their 
respective holes and a straight edge is placed against their 
P flattened faces, it will serve for locating the base or the cen- 

ter line of the plate, for marking off and laying out the dowel 
pin holes, arranging the patterns and checking off all work relating 
to it. 




542 



Moulding Machines 



The exact location of the center of the plate, and likewise the center of 
the flask, is found by dividing the base line from center to center gnjde- 
pin hole into two equal parts. Let us drill a hole C in this place (Fig. 
205), and let this hole serve as the starting point for future operations. 
Now we will assume that we have procured a tri-square with a row of 
holes drilled in each of its legs; these holes are spaced equally — say 




Fig. 205. 

I inch apart — care being taken that each row stands exactly in a 
straight line, and that both rows include an exact angle of 90 degrees. 
We place this square in such a manner on our plate that the hole in its 
apex corresponds with the center hole C of our plate, and insert a good 
fitting dowel pin through both. Thus we are able to shift the square 
over the whole surface of the plate by turning it around the center pin. 
Next we bring one leg of the square over the base line of the plate and 
insert a second dowel pin (which may be shouldered if necessary) through 
G into the corresponding hole of our square. Secured in this manner 
the square should be absolutely rigid and should not shake to right or 
left on the surface of the plate. We now drill one hole each into the 
plate through the guides H and 7 of the square, then we remove the pin 
from G, turn the square around the center pin over 90 degrees, so that 
one of its legs points upward and the other one to the left, insert a dowel 
through the hole in the leg pointing upward into the top hole I' of the 
plate, and drill the hole H^; finally we turn it again over 90 degrees, 
secure it in the same manner as before, and drill the hole P. Fig. 205 



Jigs 543 

Illustrates the square in the first position as located on the plate; the 
holes H^ and P, which are drilled subsequently, are shown in faint lines. 
In the future, we shall, call these holes "pilot holes," in order to dis- 
tmguish them from others in the same plate. These four pilot holes 
include an exact rectangle or square, and each opposite pair is located 
at uniform distances from the center of plate and flask. It will be under- 
stood that it is not absolutely necessary to employ the square for drilUng 
the pilot holes. For instance, after one plate has been prepared in this 
manner, this plate can serve as a jig for drilling any number of additional 
plates in the same manner by a single setting. Such an original or 
master plate is especially serviceable, if all holes are provided with good 
steel bushings. The pilot holes in connection with the center hole will 
serve us hereafter as guides for locating pattern dowels. 

Our object in view is to use this plate as a base for any and all suit- 
able patterns, and as an illustration we will arrange it for the reception 
of patterns of a globe valve and a bib cock. We wiU assume that the 
patterns are aU in good shape and properly parted. However, they 
shall originally not have been intended for use with either moulding ma- 
chine or drawplate. Our plate and flasks are of a suitable size, but the 
job is in a hurry — as all jobs are — and we must get out quite a num- 
ber of these castings to-day. What are we going to do about it? Take 
my advice and make it in the old fashioned way, unless you are pro- 
vided with a suitable jig plate and an inexpensive, but a good small 
driU press, which was never used by your blacksmiths or yard laborers, 
but was expressly reserved for this purpose only, was always under the 
care of a mechanic who understood how to handle it, and who took pride 
in keeping it in good shape. 

This jig plate (Fig. 205) should be provided with a number of holes, 
two rows of which, at least, are drilled exactly in the same manner as 
those in the above-mentioned square; the balance is laid out prefer- 
ably, but not necessarily so, in straight and paraUel hues, all equidistant 
from each other. Its dimensions should be sufficient to cover one 
corner, or one-fourth of your pattern plate. 

If these things are part of your equipment you will have easy sailing, 
and you wiU be better fitted to tackle the job than your competitor. 

Place this jig in such a manner in one corner of your draw plate that 
the hole (Fig. 205) corresponds with the hole C in its center; hold both 
together with dowel pins inserted into the pilot holes, and drill the holes 
through the jig into your plate, which are required for securing the 
patterns in the predetermined places. To avoid mistakes be sure that 
the hole in that particular corner of the jig, which corresponds to the 
one described as located in the apex of the square is distinctly marked 



544 



Moulding Machines 



on both sides of the jig plate — in our figure marked — and note 
carefully which holes in the jig were used for drilling the dowel holes 
into the pattern plate. Thereafter turn the jig upside down on the 
pattern plate, insert the dowel pins again through the same holes and 
01 into C and /', and the third one through OH into H^, and then, as 
before, drill through the same guide holes of the jig the corresponding 

dowel holes into the second quarter 
of the pattern plate. Repeat the 
same process at the lower half of the 
plate, being always careful that C and 
remain together and your plate is 
ready to receive the patterns. 

That there may be no doubt as to 
the method of operation, I suggest 
that you will refer to the two plates 
which are attached hereto, one of 
which (Fig. 206) is made on transpar- 
ent — so-called "onion skin" paper. 
The cut on the latter represents the jig. In faint lines thereon is shown 
the outline of the position of patterns, which corresponds to the arrange- 
ment of the same on the pattern plate (Fig. 207). Horizontal and vertical 




Fig. 206. 




Fig. 207, 

lines, which are provided with identification marks, cross all the holes 
in the jig plate. The holes which are to be used in this special case as 
guides for drilling the necessary dowel pin or screw holes in the pattern 
plate are indicated by circles drawn in heavy. Thus, the holes // X 
and 8* are used for securing the globe valve body pattern, II + and 



Jigs 545 

/// 1 1 for the body of the bib cock, and so forth. By placing the onion 
skin in such a manner over the drawing of the pattern plate, that its 
hole corresponds with the center hole C of the latter, and 01 and OH 
respectively with /' and H', it will be noticed that the outlines repre- 
senting the patterns cover each other in both cuts. The jig placed in 
this position over the pattern plate, and secured to it by the pilot pins 
at 0, 01 and OH is used in this manner for drilling all dark lined holes 
in the right-hand upper corner of the draw plate. This being done, the 
pilot pins are withdrawn and the jig plate is reversed and turned into 
the upper left-hand corner of the pattern plate, just as if it were hinged 
at the line 01; the pilot pins are replaced into the same holes of the jig 
as before and in this position they will secure it to the pattern plate by 
entering its pilot holes C, I' and H"^. It will be observed that in this 
position also, and equally well, the outlines of the patterns in both cuts 
fall exactly together. The jig is used in this position as before, the same 
guide holes which were used in the first position in the upper right hand 
corner serve again as guides for drilling the second quarter of the pattern 
plate. Identically the same process is then repeated at the lower left 
hand and lower right-hand corners of the plate, by first turning the jig 
plate around the imaginary hinge center OH, and then around 01. 

In order to prepare the patterns to suit the above conditions, we pro- 
ceed exactly in the same manner, by securing one-half of each separately, 
and always the one which has the dowel holes, at the previously deter- 
mined place on the jig plate and drilling clear through them the holes 
which coincide with those drilled previously into the pattern plate. 
The second halves of these patterns are then placed in position against 
the first (drilled) halves; they are prevented from moving sideways by 
their original dowel pins, and they may be held together by suitable 
clamps. These clamps are preferably made of a universal type which 
adapts them for use with all kinds of patterns, their lower portion being 
constructed in the shape of a frame which rests on the table of the drill 
press without rocking and which is adapted for fastening the patterns 
in such a manner that their parting faces stand parallel to the drill 
table. The half of the pattern which has been drilled first with the aid 
of the. jig occupies the upper position in this clamp or drill frame, and 
the holes in this one will now serve as guides for the drill to drill the 
holes in the second half which stands directly underneath. Finally, 
have the original dowel pins of the patterns removed and fasten all 
parts separately in place on the pattern plate by either dowels or screws, 
or both, whichever may be preferable and most convenient in your 
particular case. 

If I may call your attention again to the drawings, you will observe 



546 Moulding Machines 

that we have prepared the pattern plate in this manner with four com- 
plete sets of patterns; yet we have used only two. The castings result- 
ing from the use of these plates should be perfect as to match. The 
amount of labor required to withdraw the patterns from the sand is 
reduced to a minimum; additional time is saved by the use of a station- 
ary gate or runner on the plate, and double the quantity of castings can 
be produced in this manner with the same number of patterns and in 
the same number of flasks. All this can be accomplished by making 
an effort of no longer duration than it took to describe. 

If you have followed the above description carefully, you may have 
noticed that it is not necessary to have an individual plate prepared for 
each set of patterns. Yet I thought it better to describe this method 
of preparing pattern plates, and patterns for plate moulding in detail, 
than to leave room for any doubt or error. You can easily see that much 
of the time which it apparently took to get the plate and patterns ready 
for the moulder, can be saved by providing the entire surface of the plate 
with dowel holes before putting it into use. This should be done with 
the aid of the jig and in identically the same manner as has been suffi- 
ciently explained in the foregoing. Thus, only new patterns have to 
be prepared for the purpose, and all others, which once have been fitted, 
are easily replaced and secured to their correct positions on the plate, 
providing their dowel holes were promptly provided with specific nimi- 
bers, letters or identification marks. The additional holes, in the plate 
will not impair its working qualities, but they could be easily closed 
up with bees- wax if objectionable. Finally, it is well to note that 
each plate can be used in connection with all patterns within its range, 
and that it can be kept in continuous service, while the patterns may be 
changed at will, and as often as desirable. 

While the above description may appear somewhat too extended, I 
assure you that a serious mistake would have been made had the sub- 
ject been slighted merely for the sake of brevity. At the same time I will 
say in justification of my apparent digression, that my original subject 
has not been sidetracked. At first sight, it may appear, that the con- 
struction and the manipulation of pattern plates has but little connection 
with moulding machines, but I hope that I will succeed in showing in 
the course of this work, that they are not only intimately connected with 
each other, but that they are in fact the principal parts of all moulding 
machines. The lack of intimate knowledge of how to make use of them 
to the best advantage, the want of proper means to effect this purpose 
and the wretchedly little effort which is made to catch the right spirit of 
their nature is generally the reason why a moulding machine becomes an 
elephant on the hands of a moulder and an eyesore to its owner. 



Flasks 547 

Flasks 

Good flasks are especially important in machine or plate moulding. 
To insure good results from moulding machines the flasks must be prac- 
tically perfect. They must be constructed to insure firm holding of 
the moulding sand; must be stiff, light and durable. 

"The pins must be accurately fitted. The flasks, if made in sets, 
must be absolutely interchangeable. The pins should be square with 
the flask surface, must not bind and still must not fit too loosely. 

Copes and drags when assembled, must not rock or shake sideways. 

Wooden flasks, such as are used in most foundries, are not likely to 
give good results in moulding machine practice. However, if carefully 
and substantially made, there is no reason why their application in 
machine moulding shoiild be absolutely condemned. ' 

Iron flasks are always preferable, especially since they do not shrink, 
warp or get out of joint. " 

Pressed steel flasks are still more desirable. 

If wooden flasks are used the}^ should be faced with an iron ring, 
this ring serving not only to maintain alignment, but also as a base for 
securing flask pins. Taper steel pins secured to lugs by nuts give best 
satisfaction. The holes in lugs on drags may be reamed tapering and 
the lower ends of pins turned to fit, and tapped lightly into place. After 
the flask is closed and clamped these pms may be 
removed, thus making a few pins serve for any 
number of flasks. When not in use they should 
be removed from the flasks and properly taken 
care of. The pins are sometimes cut away so as 

to give them a triangular cross section, so that sand adhering to them 
may not interfere with readily inserting them in the holes. 

By continued use the pins and sockets are so worn as to be unservice- 
able. The pins, of course, are replaced by new ones, but the sockets 
must be bushed by sleel thimbles. The old holes are drilled out to 
standard size, so that the thimbles may be interchangeable. It is 
advisable to have the pin holes bushed when the flasks are made, so as 
to avoid subsequent annoyance. 

"The makers of moulding machines are undoubtedly very well aware 
of all the requirements which are covered by the observance of these 
little details. They wiU appreciate their importance and must admit 
that they are essential to make their machines a success. Yet to my 
knowledge these facts have never been mentioned. Is this information 
kept from the foundry man purposely, that he may not be scared from 
the purchase of machines? If he should be told all this he might in the 
first place think of the expense, and next that bis moulders cannot get 




548 Moulding Machines 

used to refinement of this kind, which by the way is not a very creditable 
opinion. But if he buys one or more of the machines oSered, he cannot 
help finding all this out before long, to his own chagrin. He may tjirow 
the machines away, or persist in the use of them and pay dearly for his 
experience. All this vexation could have been prevented in the first 
place and at a reasonable cost, had he been furnished in connection with 
the machine, with jigs, sample flasks, pins, etc., and above all. with the 
necessary information to which he was entitled." Many failures to 
introduce and maintain labor-saving devices can be traced to the lack 
of intelligent instructions sent with them. 

Mr. Stupakoff further discusses in detail the different kinds of ma- 
chines remarking: "It is a grievous mistake to think that a moulding 
machine of any description will replace a skilled moulder. There is no 
less ingenuity required to produce good castings on a machine than to 
make them by hand. 

"A moulder is aided by his experience and by his good judgment, A 
machine hand (customarily selected from unskilled labor) has nothing 
to offer but his muscle and good will. These qualities . . . are but 
poor substitutes for the dexterity of an expert. Therefore, imder 
ordinary circumstances the chances are but slight to obtain good cast- 
ings and good results by mechanical means which are imperfectly under- 
stood and subject to reckless abuse by hands which are unquestionably 
green in the business. 

Owners of moulding machines should not expect marvels from an 
inert piece of mechanism, but it is safe to say they will seldom fail in 
their calculations if they are satisfied with a reasonable increased pro- 
duction, provided they are willing to pay the best possible attention to 
their manipulation." 

Messrs. McWilliams and Longmuir in discussing the advantages of 
moulding machines conclude their remarks as follows: 

"With ordinary small work, such as is usually included in boxes up 
to 14 inches by 16 inches, the greatest time consumers are (i) ramming, 
(2) jointing , and (3) setting cores. Jointing is largely obviated with 
a good odd-side, and altogether so with a plate. Ramming by the aid 
of a press reduces the time occupied to that required for the pulling 
forward of a lever. 

Obviously, then, the greatest time consumers, with one exception, 
may be very considerably reduced by the simple and inexpensive aid 
offered by plate moulding and the hand press. " 

The exception referred to is that of setting cores, which holds good 
with all forms of mechanical moulding. Pattern drawing does not take 
up so much time as is usually supposed. With machines, jointing and 



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(549) 



550 Moulding Machines 

pattern drawing are eliminated and in certain cases, the initial outlay 
is comparatively small. 

On standard, but changing work, our best results in machine prac- 
tice have been obtained from the hand press supplemented, in case of 
deep patterns, such as flanged valve bodies, etc., by the hand rammed 
pattern drawing machine. Accessories in either case are not costly; 
the output is high and the quality good. Our best results on standard 
work, in which one plate could be run for at least 300 moulds, have been 
obtained from a pneumatic vibrator machine. 

If the same plate could be run over a period of four or five days 
without changing, then production costs fall very considerably. . . . 

Whatever may be said to the contrary, stripping plate machines 
involve costly accessories, but this outlay is warranted if the patterns 
are of a sufficiently standard character. These machines are especially 
good on intricate patterns, such as small spur wheels or others having 
little or no taper on the sides. While hand machines of any type 
represent a low first cost, the cost of subsequent accessories must not be 
forgotten. 

Power machines represent a higher initial and maintenance cost, 
but if they can be maintained in constant operation, they give a low 
production cost. Finally, the chief drawback to the further develop- 
ment of machine moulding of any type occurs in core making and core 
setting. 

An improvement in the mechanical production of irregular cores will 
result in a very considerable advance in machine practice." 

The following remark is quoted from page 131, same book: 

"As a rule we have found that while the initial cost of the machine 
is not considered, the after cost of the accessories is cut down to the 
narrowest possible margin. This is short sighted for if mechanical aids 
are adopted, there must be no half measures, or failure will inevitably 
follow. It cannot be too strongly urged that the cost of a machine 
represents only the beginning of expenditure." 



CHAPTER XXIV 

CONTINUOUS MELTING 

There are some large shops where the processes of melting and mould- 
ing are carried on continuously. In some instances the moulds are made 
in one department, taken on trucks to the neighborhood of cupola, 
where they are filled; then to the dumping floor where the flasks are 
knocked out, and sent along on same truck to moulding floor. The 
manner of conducting this operation at the Westinghouse Foundry is 
described by Mr. Sheath, and is given in substance further on. In 
other shops, where work of the character of iron bedsteads is produced, 
the operation is also continuous, but the pouring is done in the ordinary 
way. 

The management of the cupola is practically the same as in the ordi- 
nary foundry, except that the melter must have means for controUing 
the blast, so that he may increase or decrease the supply of air as the 
demand for melted iron may be greater or less. The cupola is run con- 
tinuously from 7 A.M. to 6 p.m. with an interval of one hour at noon. 

In respect to the cupola Mr. Sheath's advice is: "See that the coke 
bed is burning evenly all around, then charge just as you would for an 
ordinary run, allowing an extra amount of coke for the dinner hour. 
After running about an hour open the slag hole and keep it open, except 
during the dinner hour. Use about 40 to 50 pounds of Hmestone to the 
ton of molten metal — better use too much than too little. Have the 
cupola shell large enough, as it is easy to put in an extra Hning for smaller 
heats." 

"The Westinghouse Company have in their foundry at Wilmerding, 
Pa., three cupolas, one 60 inches, two 70 inches, inside lining. When 
running full, i.e., night and day, we melt 280 tons, running each cupola 
about ten hours. We have operated one cupola from Friday night at 
6 o'clock, until Saturday noon the following day, closing down at 
II P.M. for one-half hour for lunch, and again at 6.30 in the morning for 
three-quarters of an hour for breakfast. This is rather hard on the 
lining so we do not make a practice of it. We have tried a great many 
experiments with cupolas, but as yet have been unable to find any that 
will give better results than the double row of tuyeres. It is not neces- 
sary to keep the upper ones open all the time. Our blast pressure is 

551 



552 Continuous Melting 

about II ounces in the cupola bustle. When running full we melt ten 
to eleven pounds of iron to one pound of coke. . . . 

All charges are the same from beginning to the end of the heat. 

As the iron must come very soft and uniform we do not charge more 
than 4000 pounds at one time. 

In the discussion of his paper at the Cincinnati meeting of the Amer- 
ican Foundrymen's" Association, May, 1910, Mr. Sheath gave much 
interesting information, which is summarized briefly. 

Blast pressure, 11 ounces. 

Little metal is held in cupola, consequently tuyeres are very low. 

We are ready to tap almost after the whistle blows in the morning. 

The melting is fast or slow as the moulds appear for pouring. 

More coke is used for a small heat and slow melting, than with a 
large heat and rapid melting." 

The sand is conveyed to the moulding machines by overhead recipro- 
cating conveyors. Mr. Sheath's description of the pouring table is 
as follows: 

"I might describe how we handle what we call our No. 2 table for 
No. 2 work. On that table there are castings, a great many of them 
measuring only a few inches. Notwithstanding the small size of the 
castings, we were running. 5 2 tons ojff that table alone on a lo-hours rim, 
showing what a great amount of metal can be used up under the con- 
tinuous process in pouring small castings. We move the table at the 
rate of 20 feet per minute. A drag is put on. There are cores in it. 
As it passes up the core setters set the^ cores. Then the cope is put 
on. It then goes around to the casters in front of the cupola, which is 
connected with an endless control system. The casters have a ladle 
which can be raised or lowered by hand. They step on the table and 
travel with it, pouring anywhere from two moulds to a half dozen or a 
dozen, and by the time they are poured oE, they are off at that end, and 
they can ride back to the cupola. " 

They do that all day long. The table is not supposed to stop, 
but just goes right straight ahead. It moves at the rate of about 21 feet 
a minute, which allows them to core up, cast, cover down and all. The 
core-setters walk with the platform and become veiy expert. 

In some moulds we put in eight cores and two or three anchors 
at the same time, and it would take more than one man to do the 
coring. 

Sometimes one man will core it, sometimes it takes two. The 
casters move right along with the table, take their ladle, and travel with 
it, the same as if they were on the floor. 

One man handles a ladle that holds from 60 to 70 pounds. 



Continuous Melting 4 553 

The sand does not ball up, because we do not carry it very far 
with the conveyor. In the iron foundry from the time we make the 
mould and pour, until the mould is shaken out, that same sand is back 
again in twenty minutes. The sand is not touched by the men in any 
way. It simply goes down through the conveyor. The sand drops 
through the grating and is wet there and then taken overhead to the 
machine. 

The lowest we have ever run was 40 to 50 tons. We have run as 
low as 5 tons an hour. This takes a little more lining up. 

The economy comes in the room occupied by the moulds and the 
handling of the sand. The sand that we pour into, is back to the ma- 
chine again in twenty minutes. We get the sand, the flasks and every- 
thing back empty every twenty minutes. There is a very httle jarring 
about the platform. We have rebuilt one after running it nineteen 
years. 

There is very little shake to it if it is working right. We use both 
the hydraulic and pneumatic moulding machines. ... 

The cutting of the cupola lining as compared with ordinary practice 
varies in proportion to the length of time in blast. We do not have 
any trouble from slag. At 12 o'clock all the metal Is tapped out. We 
tap for slag twenty minutes before twelve and run it all out. The 
blast is shut off and metal run out before twelve. All the openings are 
stopped up. Very little iron comes down after the blast is stopped. 

The cupola is drained before starting to work again and the blast 
put on at full pressure so as to heat up quickly. Perhaps 300 pounds 
metal is pigged before operations are resumed. 

The smallest output any one day was 50 tons. I do not consider 
that the continuous process would pay if the production was as low as 
20 or 30 tons per day. If there were no moulding machines the process 
would be economical upon a basis of two tons per hour." 

When asked as to injury from jarring, Mr. Sheath replied: 

"We make some moulds that have thirteen pockets hanging down in 
our smooth moulds; but there are much larger moulds which we have not 
put on the table at all, because our green sand cores are just held by a 
few fingers, and we would not risk putting them on. But we make 
lots of moulds that have quite deep pockets hanging down, and there is 
very little jarring to it. The table has a slow movement which ehmi- 
Dates jarring. 

The displacing of the sand in the mould gives very little trouble. 

Xhe continuous system is adapted only for heats where the metal 
is of same character throughout. If two grades of metal are used they 
should be melted in separate cupolas. 



554 I Continuous Melting 

The moulds may be made by machine or on the floor, and the table 
used for pouring anything placed on it. 

Our conveyor makes a complete revolution in twenty minutes. We 
find in our hne of work that the moulds and castings will be cold enough 
by the time they travel to the shaking out end. 

The flasks are all iron and when shaken out are immediately put 
back on the table and carried to the moulding machine. They are 
carried entirely by the conveyor. 

Our castings are not heavy. The sand is hot when it is shaken out, 
but when it is wet and elevated and shaken back and forward in the 
reciprocating conveyor, by the time it gets to the machine and iron 
patterns it is all right. We have to keep the patterns warm to prevent 
the sand from sticking to them. 

Cores placed in hot sand will draw dampness. This feature was 
provided for. Our heaviest work is with flasks containing two castings 
which together weigh 45 pounds. Other flasks contain from thirty- 
two to forty castings, weighing a few ounces each. 

I am familiajr with a foundry where the cupola is 36 inches inside the 
lining. It is run from 7 a.m. to 5.30 p.m., continuously. The product 
is 60 tons per day. The sand is conveyed from the shaking out stand to 
the machines. Casting is continuous. 

I am imable to say how small an output could be economically pro- 
duced by this system. My experience is on a production from 50 to 
280 tons. With us the casters do nothing but cast, the machine men 
do nothing but mould and the shakers-out do nothing but shake out. 

We have had no trouble with freezing at the tap hole during the 
noon shut down." 

As regards melting losses, Mr. Sheath was uncertain whether there 
were records or not. His opinion was that it runs from three to four 
per cent. The gates and sprues are returned to the cupola without 
cleaning. 

"The pouring is done by a man moving with the table. The table 
is large enough for a man to stay on it with the mould. There is an 
overhead traveler, which travels with him as he is pouring. As soon 
as he has poured off and is at the end of his trolley line, he steps off the 
table and comes right back to the cupola. The coring is done by men 
standing and dropping in the cores as the moulds pass, or maybe taking 
a couple of steps, depending on the number of cores. The table does 
not stop from 7.15 a.m. until 12 m. miless for some special cause." 

Mr. G. K. Hooper, in the discussion on Mr. Sheath's paper, remarked 
in response to the inquiry as to the minimum production for which the 
continuous process can be economically employed: 



Multiple Moulds 555 

"That it was not so much a question of tonnage as of the number 
of moulds to be poured. " The handUng of a smaller tonnage than that 
mentioned by Mr. Sheath, if distributed over a large number of moulds 
would unquestionably be productive of great economy if performed 
mechanically and continuously. The mould is the unit which must be 
employed in determining whether the continuous system can be applied 
to any particular production." 

Mr. Hooper also states that 20 minutes are not necessary for the 
manipulation and cooling of the sand. He had experience with a 
plant where the sand was returned in six minutes. 

His further experience is that the foundry losses are less than are met 
with in the same class of work made on the floor. 

Belts are more desirable than conveyors for moving sand. Rubber 
belts are better suited for the purpose than canvas. Flat belts are 
better than those which are troughed, and wide belts moving slowly 
are better than narrow ones at high speed. 

A drag or scraper conveyor is the best for distributing sand to the 
hoppers over the moulding machines. It is preferably made of wooden 
troughs and flights. 

Nettings, riddles, sieves, bolts and nuts are best made of phosphor 
bronze. 

It is possible to handle all the sand required by productions up to 
100 tons of castings per day, or more, with two men; even though as 
much as 100 tons of sand per hour may be passing through the system. 

He has subjected moulds to very rough treatment to determine the 
liability of injury from jarring and confirms Mr. Sheath's statement 
that no trouble arises from this cause. 

Mr. Hooper commends a system wherein the moulds are carried by an 
overhead trolley and allowed to swing freely except at the point where 
the pouring was done. Less power is required, less wear entailed, and 
the expense is less. 

The continuous system is in no sense experimental. Its worth is demon- 
strated by use through many years in many large shops. ... By means of 
mechanical handhng systems in the foundry, the efficiency of the workman 
is increased from 10 to 50 per cent. The average wage can often be re- 
duced somewhat; the foundry loss is decreased; the floor space reduced; 
in fact by such appliances only can the full capacity of moulding machin- 
ery be realized. 

Multiple Moulds 

When several moulds are stacked one on top of another and poured 
from a common sprue connecting to each mould, the . process is styled 
multiple moulding. 



SS6 



Continuous Melting 



The top and bottom sections are like the cope and drag of the ordinary 
mould; each intermediate section forms the drag for that immediately 
above and the cope for the one directly below. 

A number of these sections, perhaps eight or even nine, are piled on 
top of each other and the pouring gate extends from the top cope to the 




209. — Rathbone Multiple Moulding Machine. 



bottom drag. The special advantages of the system result from the 
reduction of floor space, the amount of sand used; the nimiber of flasks 
required, and the labor of pouring ofl". 

Mr. E. H. Mumford, in a paper presented to the American Foundry- 
men's Association, stated: "That the reduction in the amount of sand 
used and in the number of flasks is 37 per cent; and in floor space 
88 per cent below that required for ordinary floor moulding. " 



Multiple Moulds 



557 



The pouring may be done with a crane ladle; therefore, one of the 
great difi&culties encountered in pouring off machine floors is ehminated. 
The great weight of sand, together with good clamping overcomes the 
tendency of straining. 






Fig. 2IO. 



Fig. 211. 



Fig. 212. 




Fig. 213. 



Fig. 214. 



Fig. 215. 



As originally practiced this method of moulding covered the piling of 
ordmary moulds, one above the other, and pouring from a cormnon gate. 
The advantages were confined to reduced floor space and reduction of 
pouring difficulties. Subsequently each intermediate section was 
made to serve as a cope and drag; but the process was confined to pat- 



558 



Continuous Melting 



tems having plane bases, the drag having simply a flat surface. This 
limitation arose from the difl&culty encountered in obtaining good 
moulds by pressing the patterns into the sand to form the drag. Later 
it was foimd that by bringing the drag up suddenly against the presser 
head, the sand was made by its inertia to take the impression of the 
pattern equally as well as when pressed from above. The scope of the 
process was immediately enlarged and although the method is not as yet 
extensively employed there seems to be a reasonable probabihty that 
it may be extended to cover the range of moderately small work now 
made by mechanical processes. 

The cut above (Fig. 209) shows a machine of this character designed 
for making chilled plow points. 

The moulds in position for clamping, and samples of castings made 
are shown in cuts above (Fig. 210-215). 

Permanent Moulds 

Moulds of more or less permanency made in loam, and moulds for chilled 
work, such as car wheels, etc., have long been in use, but moulds of a 
permanent character have only recently been used for extended lines 
of castings which are not chilled. 

The management of the cupola, melting and pouring are very much 
the same as pursued in the continuous process already described. 

The moulds are either mounted on frames near the cupola or are placed 
on revolving tables. 

The iron from which the moulds are made must be soft enough for 
machiDing; it must be strong and of suitable composition to stand 
repeated heating without warping; it must also have a close structure 
to withstand the abraiding action of hot metal. The moulds are very 
heavy so that the mass of iron may carry away the heat rapidly from 
the casting and at the same time not permit its temperature to rise 
above 300° or 400° F. Keeping the temperature within these limits 
reduces the frequency with which the mould may be used. The moulds 
are machined at the joints and preferably hinged; the outside of. the 
lower half of mould is also machined on the bottom. 

Mr. Richard H. Probert of Louisville, Ky., in a paper read at the 
Cincinnati meeting of the American Foundrymen's Association gave 
the following analysis for moulds which had given good results: 



Si 


s 


Phos. 


Mn 


C. C. 


G. C. 


2.02 


.07 


.89 


.29 


.84 


2.76 



Permanent Moulds 559 

He also states that he had used moulds made from high carbon steels 
for castings having sharp thin projections. In constant use these moulds 
become roughened, but are not burnt or eaten away, as with cast-iron 
moulds. 

He likewise suggests that pressure applied to the moulds immediately- 
after pouring would result in castings presenting sharp clean lines of 
great density and strength. 

Mr. Edgar A. Custer of Tacony, Pa., presented at the same meeting 
a most interesting paper on the same subject and also submitted many 
sample castings, made by this process. Without giving definite informa- 
tion as to sizes of moulds with respect to patterns, he impressed the 
necessity for great mass in them. For instance, a mould for a 2-inch soil 
pipe T, weighs 500 pounds; one for a 3-inch trap 1700 pounds. In a 
mould for 4-inch soil pipe weighing 65 pounds, there were 6500 pounds 
iron. Castings were made in this mould every seven minutes without 
raising its temperature over 300° F. 

He found that it is imnecessary to coat the moulds, but that their 
temperature must be sufficiently high to prevent the condensation of 
moisture before casting. If the castings are removed from the moulds 
immediately upon setting, there is little trouble about sticking after 
60 to 100 castings have been made. The moulds improve by continued 
use, but how long they will last is unknown. He has now in use a mould 
in which 6000 castings have been made and it shows no signs of deterio- 
ration. The life of a mould depends not so much on the number of cast- 
ings made in it as upon the number of times it has been allowed to 
become entirely cold and then reheated. Continuous pouring, when 
correctly timed so as to preserve a generally even temperature, has but 
very slight tendency to crack the mould. If the castings are rem.oved 
from the mould as soon as they have set sufficiently to handle, there is 
with proper mixture no appearance of chill when cold. This was shown 
by a number of samples which had been machined. The iron was soft, 
and was readily filed on the parts not machined. 

Cores are made of cast iron, and if straight, or curved in circular 
shape, can easily be removed from the castings, if taken out quickly 
while the casting is at a bright red. It is altogether probable that the 
time to remove the castings is at any period after setting and prior to 
the third expansion, and that the core should be removed during the 
third expansion. See Keep's "Cast Iron," Chapter \TII. The iron 
must be melted very hot. Mr. Custer's view is that the percentage 
of silicon may range between 1.75 and 3 per cent. The mixture in use 
by bim is as follows: 



56o 



Continuous Melting 



Si 


Phos. 


s 


Mn 


G. C. 


C. C. 


2.24 


1. 12 


.01 


.38 


3.02 


1.54 



Mr. Custer summarizes as follows: 

"Any casting that can be poured in a sand mould can be poured in an 
iron mould. If the iron is hot enough to run in green sand mould it will 
surely run in an iron mould. 

Iron that is suitable for radiator fittings, or brake shoes, or any 
other class of duphcate work that -is made in sand, will be suitable for 
the use of permanent moulds. The same experience that shows the- 
f oundryman what is best for sand moulding can be applied in permanent 
mould work. 

It is true that a somewhat wider range of iron can be used in per- 
manent moulds for the same class of work than is the case in sand mould- 
ing, but any change from the general practice in selecting irons for any 
particular class of work must be made with a great deal of care. It is of 
course a subject that demands close and incessant study, and every 
manufacturer who wishes to use permanent moulds must give the same 
care and thought to this method that he has given to those previously 
employed. " 

Interesting information was brought out in the discussion of -Mr. 
Custer's paper which is summarized below. 

Temperature of moulds is not allowed to exceed 300° F.; the pouring 
is proportioned at intervals so as not to exceed that temperature. 

It takes 25 seconds to make a 4-inch soil pipe T. No sand used in 
the core. The core for this mould was shown, which had been in con- 
stant use for thirteen months. 

The mould for a 2-inch T weighed 500 pounds, the T itself weighs 
8^i poimds. 

The core with which the T was made was shown. It had been in use 
seven months during which period 3500 castings were made. 

A casting can be made from it every forty-five seconds throughout 
the day. 

No precaution is taken against shrinkage. Chilling quickly to point 
of set makes castings homogeneous, reducing shrinkage strains to a min- 
imum. A trap weighing 42 pounds made on a sand core was shown. 
One is made every seven minutes. The mould weighs 1900 pounds. 
The casting is taken out within four seconds after pouring. 

No special care is taken to keep the moulds from dampness. They 
are simply wiped out carefully before using. The core, upon which a 



Centrifugal Castings 561 

four-inch pipe, 5 feet 3 inches long was made, was shown. The pipe 
was H inch thick and weighed 65 pounds. The core had Me inch taper 
in the whole length. 

The pouring table revolves once in jVz minutes. There are on it 
35 pipe moulds, and a casting is produced every fifteen seconds. 

In a ten-hour run at this rate of production, the temperature of the 
moulds never exceeds 250° F. The operations are automatic. With a 
2-inch pipe, the casting can be taken from the mould within three seconds; 
it must not be allowed to remain in mould over six seconds. With a 
six-inch pipe, the time of removal is from five to sixteen seconds. 

One man operates the table, pouring and removing the pipe, cleaning 
out the moulds, and setting the cores. The iron is white hot as it comes 
from the cupola. No attention is paid to coating the moulds; they are 
wiped out from time to time with a greasy rag if any dirt is present. 
The heaviest castings made are 6-inch pipes weighing no pounds each. 

Gates are made larger than in green sand practice. 

Mr. Custer did not consider the phosphorus content of importance. 
He prefers iron 0.5 to i.o per cent phosphorus on account of fluidity. 

Chilling occurs so quickly that there is no segregation. The tensile 
strength of castings made in iron moulds is about 30 per cent greater than 
that of same character made in sand. 

Brake shoes are left in the mould seven seconds. It takes about a 
minute to make a brake shoe. The castings do not warp. 

Six-inch pipes can be laid on the pile within 20 seconds after casting. 

The silicon content should not be lower than 1.75 per cent, sulphiu: 
should be below 0.05 per cent, total carbon high as possible not below 
2.65. 

Has used 70 per cent scrap with pig carrying 3 per cent silicon. 

Centrifugal Castings 

In 1809, Anthony Eckhardt of Soho, England, was granted a patent 
for making castings in rotating moulds, procuring in this manner either 
hollow or solid castings. Nothing favorable seems to have resulted 
from the scheme. 

In 1848, Mr. Lovegrove attempted to make pipes in this manner. 
Subsequently a Mr. Shanks patented the same method in England. 
Sir Henry Bessemer endeavored to remove the gases from steel castings 
by a similar process. 

About the same time a Mr. Needham endeavored to apply the method 
to making car wheels. So far as can be learned nothing of practical 
value resulted from these efforts. It is said that car wheels are now 
made in Germany in this way using a high carbon steel for the rim and 



562 Continuous Melting 

soft material for the center. The mould is made to revolve about 120 
times per minute while pouring. The principle is used by dentists success- 
fully, and there seems to be no good reason why it could not be applied 
to some classes of iron castings where difiSculty is encountered in running 
delicate parts, or to obtain increased density at the periphery. 

Castings under Pressure 

Attempts have been made to submit the liquid iron to pneumatic 
or hydraulic pressure in order to eliminate porosity or shrinkage cavi- 
ties. So far these have been entirely experimental; the successful 
application of the idea would remove all doubt as to shrinkage in rims 
of fly wheels or in similar castings, where undiscoverable defects may 
exist. 

Direct Casting 

Making castings directly from the furnace has been practiced more 
or less since the discovery of reducing iron from the ores. But by 
reason of the presence of impurities and gases, which are to a greater 
or less extent eliminated in the process of refining in the cupola, the pro- 
duction of castings by the direct process has never been followed to 
any extent. In fact, except for quantities of large coarse castings, or 
an occasional piece required at the furnace, it may be said that the 
process has been entirely disregarded. The presence of kish in large 
quantity has been the greatest obstacle to contend with. The use of a 
receiver with reheating provision, in connection with manganese would 
seem to indicate a solution of this difficulty, especially for pipes and 
other coarse castings, where the physical characteristics are not matters 
of vital importance. 

In view of the advancement in modem metallurgy, it is more than 
probable that commercial competition will turn manufacturers of prod- 
ucts for which such iron is suitable to further efforts in this direction. 

Carpenter Shop and Tool Room 

In every foundry the services of a carpenter and machinist are more 
or less in demand. In the larger works it is found most convenient to 
devote separate space to each. 

The carpenter shop should be given sufficient room for construction 
and repair of wood flasks, bottom boards, etc., and with its equipment 
of benches, trestle, etc., should be provided with a cut-off saw. 

The tool room should have a drill press and smaU lathe. Unless there 
is a laboratory connected with the works, the testing machines are con- 
veniently located in the tool room. 



Tumblers 



563 



The Cleaning Room 

The cleaning room should be adjacent to the moulding room, but 
separated from it by a wall or partition to exclude the dust and dirt 
from the foundry. 

Where the work is heavy there should be proper facihties in the way 
of tracks and cranes. The necessary equipment comprises tumbling 
barrels, brushes, chipping (either hand or pneumatic) and grinding 
apparatus. 

The sand blast is also of the greatest value. 



Tumblers 

The shape, size and number of tumblers depend entirely upon the 
character and volume of the work. Tumblers are made to revolve 
about inclined or horizontal axes. Those having inclined axes are used 
for very light castings, brass, forgings, etc. They are seldom found in 
the ordinary foundry. The barrel may be tilted for loading or dis- 
charging. The following cut shows the general character of this type. 
They vary in size as re- _ 

quired. 

Fig. 216 shows the No. 
2 machine mounted with 
28-inch cast-iron barrel in 
partially lowered position 
preparatory to dumping. 

This machine is designed 
along the same lines as the 
No. I tumbler excepting that 
it is much heavier and the 
crank shaft is back geared 2 
to I, making the raising and 
lowering of the barrel when 
heavily loaded quick and 




Fig. 216. 



easy. It is driven by tight and loose pulleys 16 inches in diameter by 
3M-inch face, and will take barrels from 22 to 36 inches diameter, of 
wood, cast iron, steel, wrought brass and cast brass. The tumbling 
process may be wet or dry as desired, and the design of the machine 
is such that the barrel may be located at any required angle while in 
motion, to suit quantity of work being operated upon, and lowered to 
empty by means of the crank, ratchet and pawl. It has a belt shifter 
not shown in cut. 



564 



Continuous Melting 



Floor space, with barrel, 42 by 60 inches. 

Weight, without barrel, 600 pounds. 

Speed of tight and loose pulleys, 147 to 168 rev. per min. 

Speed of barrel, 35 to 40 rev. per min. 

The ordinary horizontal tumbler is from 30 to 36 inches in diameter 
and from 4 to 6 feet long. It may revolve on trunnions or on friction 
rollers. 

The barrel is made up of cast-iron staves securely bolted to the heads, 
and with closely fitting joints. The peripheral speed should be about 
90 feet per minute. They are used singly, in pairs, or in batteries. 
The castings, large and small, are packed as closely as possible in the 
barrels, together with a quantity of shot, sprues or stars. Any im- 
occupied space is filled by pieces of wood. If any of the castings are 
dehcate they are tumbled by themselves, so as to avoid breakage. It is 
not uncommon to tumble castings weighing 600 to 800 pounds; they 
must be packed very closely, however. The length of time that castings 
must be rattled to clean them depends entirely upon the intricacy of 
the shapes. While ten minutes may answer for some, others may 
require 30 minutes or even an hour. 

The injury to castings from grinding away sharp corners or angular 
projections arises from the improper packing or too long continued 
tumbling. Since the dust comes from the tmnblers in great volume, 
as an act of humanity, they should either be enclosed, or provided with 
exhaust fans. The dust may be carried to a water seal, or discharged 
outside the shop. 

The cuts following show several varieties of tumblers manufactured. 
Usually each shop makes its own tumblers, so that the patterns may be 
at hand for repairs. 




Fig. 217. 



Reliable Steel Square Tumbling Mills 



565 



"The Falls" Friction-driven 
Tumbling Mill 

This ipill was designed by an 
expert foundryman. It is of the 
very best workmanship through- 
out, and is guaranteed to give 
splendid satisfaction. 

Made in six sizes as follows: 




No 


Diameter, 


Length, 




inches 


inches 


I 


26 


48 


2 


32 


54 


3 


38 


60 


4 


42 


54 


5 


48 


72 


6 


54 


78 



Reliable Steel Square Tumbling Mills 

Particularly Suited for Light Castings 




Fig. 219. 

This is a strong mill with double heads. Each side is strengthened 
by a T bar run and riveted the full length and doubly bolted to each 
head. Edges are enclosed by an angle securely riveted and countersunk 
from end to end. Door opening is strongly reinforced. 



566 Continuous Melting 

Friction-driven Exhaust Tumbling Mills 



Fig. 220. 

These mills are especially adapted to be run in gangs from one shaft 
and one driving pulley. They can be stopped or started independently 
or may be removed with contents from the driving frame by crane and 
conveyed to any part of the foundry. Mills may be equipped at small 
extra cost with reversing device, permitting rotation in either direction, 
miUs still remaining portable and interchangeable. 

They combine strength with simphcity. 

Mr. Outerbridge discovered that the strength of castings was increased 
by tumbhng. Following up this discovery Mr. Keep determined that 
the increase of strength by tumbling ceased after two hours treatment, 
that the increase in strength was due to smoothing and pressing the 
surface, closing any incipient cracks and openings. 

Chipping 

Much of the chipping must be done by hand. The pneumatic hammer 
has, however, superseded the hand chisel to a great extent. There are 
few foundries not equipped with this device. 

Grinding 

To finish castings properly, the fins and gate spots should be groimd. 
In addition to the ordinary emery wheel, the portable wheel driven by a 
flexible shaft is employed advantageously. 

The Sand Bliast 

This appliance is of the greates-t importance. More surface can be 
cleaned with it in a given time than by any other means except the 
rattler. The use of the other appliances above mentioned is not dis- 
placed by it, however, as there are many recesses about castings which 
are protected from the blast, and which must be cleaned by hand. 

The importance of properly cleaning castings should not be over- 
looked. No matter how well made or how good in respect of material, 
if they are sent from the cleaner in a slovenly condition, their commercial 
value is greatly impaired. 



Pickling 567 

Pickling 

Formerly pickling castings was largely employed, but of recent years, 
by reason of the improved facings used, the practice is not so much 
followed. Nevertheless there are places about castings from which the 
sand is not properly removed by the ordinary processes, and again 
some machine shops prefer pickled castings, as the cutting edges of 
their tools are not injured so quickly, by reason of the entire removal 
of the sand. This process is also followed where the castings are to be 
galvanized or tinned, as it leaves clean metallic surfaces. 

For pickling, either sulphuric or hydrofluoric acid is used, the former 
more commonly. The acid solution must be weak; one part of ordinary 
vitriol to four or six parts of water attacks the iron rapidly, whereas the 
undiluted acid has no effect. 

In diluting the acid, care must be taken to pour the acid into the 
water, and not the water into the acid. Dilute sulphuric acid dissolves 
the iron in contact, thereby loosening the sand. The action is more 
rapid with warm than with hot solution. 

This solution, when applied to castings, will loosen the sand scale in 
from one to twelve hours, depending upon the thickness of the scale. 
The acid solution is kept in a lead-hned wood vat. The vat should 
be about two feet deep, the other dimensions varying \vith the amount 
of castings to be treated. At the bottom of the vat is a wooden grating 
fastened together by wood dowels. The grating is held down by lead 
weights. It must be high enough above the boittom of the vat for the 
sand to drop through. Upon this grating the castings rest as they are 
immersed. 

After remaining in the bath the requisite length of time, they are 
removed and thoroughly washed with hot water. The acid must be 
completely removed or they will rust. It is a good plan to dip them in 
a strong solution of lye or soda before washing. 

Another practice is to place a lead-lined platform so that one edge 
may overhang one end of the vat; the platform inclining a couple of 
inches toward the vat, and having the remaining edges raised two inches, 
so that all the drainage may be into the vat. Upon this platform is 
placed a wood grating, and the castings on the grating. The pickle is 
then dipped from vat with an iron bucket and poured over the castings. 

They are washed thoroughly with the pickle, so that there may be 
no sand surface which has not been saturated. It may be necessary 
to repeat the operation more than once. When the sand scale begins 
to loosen, the castings are removed and washed as before. The washing 
may be done with a hose while the castings are on the bed, but in such 



568 Continuous Melting 

case provision must be made to carry off the water in a trough so that 
it may not enter the vat. 

The strength of the solution must be kept up by addition of fresh 
acid from time to time. 

Hydrofluoric Acid 

Where this acid is used for pickling, the solution should be one part 
of 48 per cent acid to 30 parts of water. Hydrofluoric acid dissolves 
the sand instead of acting on the iron. The treatment of the castings 
is the same as with the vitriol, but the sand must be removed from below 
the grating, otherwise the acid will be rapidly neutraUzed. 

The workmen should be cautioned in handling either of these acids 
as they cause severe bums, if they come in contact with the flesh. 
Where acid is spilled on the flesh or clothing, wash the parts freely with 
water and then with dilute ammonia. Raw hnseed oil applied to bm-ns 
produces a soothing effect. 

Hydrofluoric acid leaves the surface of the castings bright and clean, 
and is, therefore, best for electroplating. 



CHAPTER XXV 



Method of Ascertaining the Weight of Castings from the 
Weight of Patterns 





Weight when cast in 


Pattern weighing 
one pound 


Cast 

iron, 

pounds 


Yellow 
brass, 
pounds 


Gun 

metal, 
pounds 


Zinc, 
pounds 


Alumi- 
num, 
pounds 


Copper, 
pounds 




8.8 
8.5 
16.1 
10.7 
12.0 
8.5 
9.2 
9.4 
10.9 
14-7 
I3-I 
16.4 


9.9 
9-5 
18.0 
12.0 
13. 5 
95 
10.3 
10. 5 
12.2 
16.5 
14.7 
18.4 


10.3 

10. 
18.9 
12.6 

14. 1 
10. 
10.8 
II. 
12.8 
17.3 
IS. 4 
19-3 


8.5 
8.2 
15-6 
10.4 
II. 6 
8.2 
8.9 
9.1 
10.6 
14.3 
12.7 
15.9 




10.5 


Beech 


3 
5 
3 

4 
3 
3 
3 
3 
5 
4 
5 


I 
8 
9 
3 
I 
2 
4 
9 
3 
7 
9 


Cedar 


19.2 
12 8 


Cherry 


Linden 


14.3 
10 I 


Mahogany 


Maple 




Oak 




Pear... 






17. 5 

15. 6 
19-5 


Pine, yellow 

Whitewood 





Allowance should be made for any metal in the pattern. 

Specific Gravity and Average Weight per Cubic Foot of 
Pattepjst Lumber 



Wood 


Specific 
gravity 


Average 
weight per 
cubic foot, 

pounds 


Beech 


TX 


46 


Cedar 




62 
66 
60 
81 
68 
77 
74 
45 
61 
75 


39 
41 


Cherry 


Linden 


37 




Maple 




Oak, white 


48 


Oak, red 


46 




28 




38 


Walnut 


38 











569 



570 



Determination of Weight of Castings 



Weight of Castings Determined from Weight of Patterns 

(By F. G. Walker.) 





Will weigh when cast in 


A pattern weighing 
one pound made of 


Cast 

iron, 

pounds 


Zinc, 
pounds 


Copper , 
pounds 


Yellow 
brass, 
pounds 


Gun 
metal, 
pounds 


Alumi- 
num, 
pounds 


Lead, 
pounds 


Mahogany, Nassau 

Mahogany, Honduras. 
Mahogany, Spanish. . . . 


10.7 
12.9 

8.5 
12.5 
16.7 
14. 1 

9.0 


10.4 
12.7 

8.2 
12. 1 
16. 1 
13.6 

8.6 


12 
15 
10 
14 
19 
16 
10 


8 
3 

I 
9 
8 
7 

4 


12.2 
14.6 
9.7 
14.2 
19.0 
16.0 
10.4 


12.5 
iS.o 
9.9 
14.6 
19. 5 
16. s 
10.9 


SO 




Pine, white 








Oak 





Weight of a Superficial Foot of Cast Iron 



Thick- 
ness, 
inches 


Weight, 
pounds 


Thick- 
ness, 
inches 


Weight, 
pounds 


Thick- 
ness, 
inches 


Weight, 
pounds 


Thick- 
ness, 
inches 


Weight, 
pounds 




9.37 
14.06 
18.7s 
23.43 


I 

m 


28.12 
32.81 
37.50 
42.18^ 


1 3/8 
1I/2 


46.87 
SI. 56 
S6.2S 
60.93 


1% 
2 


65.62 
70.31 
75.00 



Formulas for Finding the Weight of Iron Castings 

To find the weight of square 
or rectangular castings, multi- 
ply the length by the breadth, 
by the thickness, by 0.26: 
W = LBT X 0.26. 




Fig. 221. 



To find the weight of 
solid cylinders, the weight 
equals the outside diameter 
squared, multiplied by the 
length, multiplied by 0.204: 



W 



9M\ 




^^ 




-D— >| 


[<_ L 

Fig. 222. 
D.204. 


- -H 



Determination of Weight of Castings 



571 



W = weight of casting in pounds; 
L = length of casting in inches; 
T = thickness of casting in inches; 
B = breadth of casting in inches; 
D = outside or large diameter in inches. 

To find the weight of hol- 
low cylinders, multiply the 
small or inside" diameter plus 
the thickness, by the length, 
by the thickness, by 0.817: 




W={d + T)TLXo.Si7. 



Fig. 



223. 




DdL X 0.204. 
W = weight of casting in pounds; 
L = length of casting in inches; 
T = thickness of casting in inches; 
D = large diameter in inches; 
d = small diameter in inches. 

To find the weight of a hollow hemisphere, 
multiply the thickness by the small radius 
plus the thickness divided by 2, squared, by 
1.652: 

/ T\2 

T X 1.652. 



To find the weight 
of a sohd ellipse, mul- 
tiply the large diam- 
eter by the small di- 
ameter, by the length, 
by 0.204: 





To find tl^e weight of a solid sphere, mul- 
tiply the diameter cubed by 0.1365: 

W = D^X 0.1365. 



Fig. 226. 

W = weight of casting in pounds; 

R = outside or large radius in inches;" 
r =■ inside or small radius in inches; 

T = thickness in inches; 

P — outside or large diameter in inches. 



572 



Determination of Weight of Castings 



Formulas for Finding the Weight of a Hollow Iron Sphere 
and a Body of Rammed Sand 

To find the weight of a hollow sphere mul- 
tiply the outside diameter cubed, minus the 
inside diameter cubed, by 10.365: 

W = {D^ 





Fig. 227. 

W = weight of casting in pounds; 

D = outside or large diameter in inches; 

d = inside or small diameter in inches. 



0.1365. 



To find the weight of a body of rammed 
sand, multiply the length by the breadth, by 
the height in feet, by 87: 

W = LBHX2>T. 

W = weight of body of sand in poimds; 

L = length of body of sand in feet; 

B = breadth of body of sand in feet; 
H = height of body of sand in feet. 



jMniiii 



Q!sil!!iMii.LLiLiLlICu3 

Fig. 228. 



Formulas for Finding the Weight of Iron Castings 




l<-s--H" P 



L— -.— — 

Fig. 229. 

To find the weight of a flywheel, 11 feet in 
diameter, having elliptical arms. The first 
operation is to find the weight of the hub; 
second, the rim; and third, the arms. The 
sum of these gives the weight of the wheel. 

To find the weight of the hub: 

W= (d+T)TLXo.Si7. 

To find the weight of the rim, the same 
formula as above is used. 

To find the weight of one arm : 

W = DdL X 0.24. 



To find the weight 
of a triangular casting, 
multiply the length by 
the breadth, by the 
thickness, by 0.13: 

W = LBT X 0.13. 




Determination of Weight of Castings 573 

Multiply by six to find the weight of the six arms. 

W = weight of casting in pounds; 
D = outside or large diameter in inches; 
d = inside or small diameter in inches; 
L = length in inches; 
T = thickness in inches; 
B = breadth in inches. 

To find the weight of a spherical segment of one base, multiply the 
square of the height by the difference between the radius of the sphere 
and one-third of the height, by 0.818; or, to the 
radius of the base squared, multiplied by the 
height by 0.409, add the height cubed multiplied 
by 0.136: 



W 



-(-!) 



X 0.81^ 




or 



W = r^H X 0.409 -\-H^X 0.136. 
W = weight of casting in pounds; 
R = radius of sphere in inches; 
H = height of segment in inches; 
r = radius of base in inches. 



Fig. 231. 



To 
radius 



find the weight of a spherical segment of two bases, from the 
of the sphere multiplied by the difference between the squares of 
the distances from the bases to the poles by 
0.818, subtract the difference between the cubes 
of the distances from the bases to the pole, 
multiplied by 0.273, or: 

To the sum of the squares of the radii of the 
bases, multiplied by the height by 0.409, add 
the height cubed, multiplied by 0.136: 

W = R{A^- B^) X 0.818 - (43 _ 53) X 0.273, 




^ 



Z7^ 



Fig. 232. 



TF = H (r2 + ^2) X 0.409 + i73 X 0.136. 
W = weight of casting in pounds; 
R = radius of sphere in inches; 

r = radius of large base of segment in inches ; 

5 = radius of small base of segment in inches; 
A = distance from large base to pole in inches; 
B = distance from small base to polo in inches; 
H = height of segment in inches. 



574 



Determination of Weight of Castings 



. To find the weight of a ring made by cutting a cylindrical hole through 
the center of a sphere, multiply the chord cubed by 0.136: 

W = ax 0.136. 

The chord is equal to the square root of the 
result obtained by subtracting the square of 
the diameter of the hole from the square of 
the diameter of the sphere: 




233- 



C = VZ)2 _ dK 

W = weight of casting in pounds; 
D = diameter of sphere in inches; 
d = diameter of hole in inches. 



To find the weight of a ring of circular cross section, multiply 
the radius of the cross section squared by the radius of the circle 
passing through the center of the cross section, 
by 5.140: 

W = rmx 5.140. 

W = weight of casting in pounds; 
r = radius of cross section in inches; 
R = radius of circle passing through cen- 
ter of cross section in inches. ^^^- 234. 

To find the. weight of a frustrum of a hexagonal pyramid, multiply 
the sum of the side of the large base squared, the side of the small base 

squared and the product 
of the two sides, by the 
length, by 0.226, or mul- 
tiply the sum of the dis- 
tance across the flats of 
the large base squared, 
the distance across the 






k"- 



Fig. 235. 

flats of the small base squared and the product of these two distances, 
by the length, by 0.075. 

W = {S^ + s'' -{- Ss) L X 0.226, or W = (F^ +P + Ff) L X 0.075- 

To find the weight of 
a straight fillet, multiply 
the radius squared by the 
length, by 0.0559. 

W = R^LX 0.0559. 



Fig. 236. 



Weight Required on Copes 



575 



W = weight of casting in pounds; 
L = length of casting in inches; 
S = side of large base in inches; 
5 = side of small base in inches; 
F = distance across the flats of large base in inches; 
/ = distance across the flats of small base in inches; 
R = radius of fillet in inches. 



1 


1 1 


Ci_^ 


" u ,.^ 



Formulas for Finding the Weight Required on a Cope to 
Resist the Pressure of Molten Metal; and the Pres- 
sure Exerted on the Mould 

To find the weight required on a cope to resist the pressure of molten 
iron, multiply the cope area of the casting in 
square inches by the height of the riser top 
above the casting in inches, by 0.21: 

W = AH X 0.21. "'' ' ''"'"" " 

Fig. 237. 

W = weight to be placed on a flask in pounds; 

A = cope area of casting in square inches; 

H = height of riser top above casting in inches. 

To find the pressure exerted on a mold by molten iron multiply the 
height in inches from the point of pressure to 
the top of the riser by 0.26: 

P = HX 0.26. 
.•..;.•;:••. :■^•:y.•:■.•^•v^.•L^^v.:•; P = pressure in poimds per square 

Fig. 238. inch; 

H = height from point of pressure to the top of the riser in 
inches. 



To find the weight of an inside circular fillet, 
multiply the difference between the diameter of 
the cyhnder made by the side of the fillet and 
the product of the radius and 0.446, by the 
radius squared, by 0.176, or, from the diameter 
of the cyhnder made by the side of the fillet, 
multipUed by the radius squared, by 0.176, sub- 
tract the radius cubed multiplied by 0.0784. 

W = (D - 0.446 R) R' X 0.176, 
or W = DR^ X 0.176 - R^ X 0.0784. 





Fig. 239. 



576 



Determination of Weight of Castings 



To find the weight of an outside circular fillet, multiply the sum of 
the diameter of the cylinder made by the side of the fillet and the product 
of the radius and 0.446, by the radius squared, 
by 0.176, or to the diameter of the cylinder 
made by the side of the fillet multiplied by the 
radius squared, by 0.176, add the radius cubed 
multipHed by 0.0784: 

TF = (D + 0.446 R) R" X 0.176, 
or 

W = DJR? X 0.176 + i?3 X 0.0784. 

W = weight of casting in pounds; 
R = radius of fillet in inches; 
D == diameter of cylinder made or generated by 
the side of fillet in inches. 




CHAPTER XXVI 

WATER SUPPLY, LIGHTING, HEATING AND 
VENTILATION 

Water Supply 

Provision for water supply to the foundry is a matter of the first 
importance. If water cannot be obtained from the pubUc mains, facil- 
ities for pimiping and distributing must be provided. The system 
must be so arranged, either by elevated tanks or otherwise, as to furnish 
water under a pressure of from 25 to 30 pounds. While the supply 
must be abundant, the natural tendency to its wasteful use must be 
suppressed. 




Fig. 241. — Water Box and Hose Connection. 

Conveniently located near the cupola for quenching the dump, should 
be a hydrant with hose attached, ready for immediate use. Pipes should 
be so run about the foundry that taps may be conveniently distributed 
for wetting down the floors and sprinkling the sand heaps; each floor 
must have easy access to the sprinkling hose. Ample provision should 
be made for drinking; basins near the drinking fountains, in which to 
bathe their arms and faces, add greatly to the comfort of the workmen. 

The illustrations herewith, taken from the Iron Age, show provisions 

577 



578 Watey: Supply, Lighting, Heating and Ventilation 

made for this purpose and for lavatories, etc., in a large Cleveland 
foundry 

Running water should be suppHed at the closets. In many foundries 
of recent construction, wash basins, shower baths and lockers are pro- 
vided, enabling the men to wash and change their clothes before leaving 
the works. The free use of water implies, of course, a system of sewer- 
age. Care must be taken to avoid puddles or wet spots about the floors. 
The matter of water supply for fire protection is entirely independent 
of that for foundry purposes, and should be provided for separately. 




Fig. 242. — Porcelain Washbowls and Steel Lockers in Lavatory. 



Lighting 

Next to water supply in importance is the matter of lighting. Many 
foundries are deficient in this respect and suffer either in the character 
or quantity of product from improper lighting. Daylight is invaluable, 
and should be utilized to the fullest extent. In the construction of 
foundry buildings, the windows should be tall and as close together as 
the character of the structure will permit; they should not extend 
lower than four feet from the floor. A modem construction showing 
the sides of the building made almost entirely of glass is shown in the 
engraving below. 

Windows in the moniter should be swiveled and arranged to open easily 
for ventilation. Skylights are to be avoided if possible, as they cause 
no end of annoyance. The weaving-shed roof gives excellent results, 
and is frequently used in foundry construction. The glazing should be 
of a character to prevent the direct admission of sunlight. Ground 
glass, wire glass or glass with horizontal ribs afford a mellow light, 
relieving the eyes from the glare of direct sunlight. 



Heating and Ventilating 



579 



Artificial light for the early morning and late evening hours, during 
the season of short days, is best aflforded by some adaptation of the 
electric lamp. Tungsten lamps in groups of four, distributed at inter- 
vals of about 40 feet are largely used. Such lamps are provided with 
reflectors to direct the rays downwards and diffuse them. The lamps 
must be placed so as to clear the crane ways, and should be elevated 
about 20 feet from the floor. The Cooper-He we tt mercury lamps, 
placed about 50 feet apart and covered with reflectors, are very satis- 
factory. The flaming arc lamps, similarly placed, furnish the greatest 
illumination for a given expenditure of current. 







, Fig. 243- 

A recent type of kerosene burner, the Kauffman, having a mantel 
somewhat similar to the Wellsbach, is said to furnish a given candle 
power at less cost than any tamp known. 

With any system of lighting, care must be taken to keep the lamps 
clean and in good order, otherwise their efficiency is soon greatly im- 
paired. Where electric hghts are used, the generators should be inde- 
pendent of those which furnish current to the motors. Power for fans, 
elevators, cranes, sand mixers, etc., is most conveniently supplied by 
electricity. Each machine should have an independent motor. Elec- 
tric trucks, operated by storage batteries, and magnetic hoists, for 
service in the foundry and yard are almost indispensable. In fact 
the introduction of electricity has so simplified foundry operations 
that its use is imperative. 

Heating and Ventilating 

Heating and ventilating the foundry are subjects which formerly 
received little attention. A few stoves or open fires in iron rings, placed 
where they would be least in the way, constituted the usual equipment; 
foundries fitted with steam heating or hot-air systems were exceptional, 



580 Water Supply, Lighting, Heating and Ventilation 

Gradually foundrymen have learned to appreciate the advantages of a 
comfortable •working temperature and good ventilation, as shown by 
increased output. A cold shop and chiUed or partly frozen sand heaps 
may easily reduce the value of a morning's work from 20 to 25 per cent. 
As foundry operations require active physical exertion, the temperature 
of the shop should not exceed 50° to 55° F. At 7 o'clock in the morning 
the building should be warm throughout. "For this purpose direct and 
vacuum steam heating systems are used with good results. Both are 
open to objections. The warm air is not evenly distributed; much of 
it is sent to the upper part of the building, where it does no good. With 
either system several hours are required in extremely cold weather to 
produce a comfortable temperature in the morning. Cold air enters 
through the windows and doors, causing drafts and an uneven distribu- 
tion of heat. 

More satisfactory results are furnished by the fan and hot-blast system. 
This consists of a sheet-iron chamber, in which are placed the requisite 
number of coils heated either by direct or exhaust steam, if the latter 
is available, an exhaust fan and the distributing pipes. The fan draws 
the air over the coils and from the chamber and forces it about the build- 
ing through large ducts, from which branch pipes are taken at proper 
intervals; through these branches the warm air is discharged at the 
desired spots within the shop. This system is largely used and possesses 
advantages over those having direct radiation. 

The amount of heat absorbed by air flowing over pipes increases 
rapidly with the velocity of the air. When the velocity of the air current 
flo\ving over the pipes in the heating chamber is about 1500 feet per 
minute (the usual velocity) the area of the heating surface required to 
accomplish a given heating effect is only about one-fifth that for direct 
radiation. With the fan and hot-blast system the building is filled 
with air under slight pressure, termed a plenum, which prevents cold air 
from entering; warm air flows out through all leaks. The warm air 
is discharged from the pipes near the floor, and uniformly distributed 
through the lower part of the building. By reason of such distribution 
and the great volume of air discharged, the shop may be quickly warmed 
in the morning. If the fan is driven by an independent engine, the 
exhaust steam is sent directly to the coils, thereby making the expendi- 
ture for power nominal. Where live steam is not available for an engine 
the fan may be driven by a motor. With the motor-driven fan, the 
watchman can start the apparatus during exceedingly cold nights, and 
thereby prevent the sand heaps from freezing. The ducts are usually 
circular in section, made of galvanized iron and supported by the chords 
of the building so as to clear the crane'way. 



Heating and Ventilating 



581 



The sketch below shows the usual arrangement for fans and ducts. 
In shops of moderate size, where but one fan is required, the ducts, ©f 
course, must nm all around the building. 






Fig. 244.— Typical Arrangement of Heating and Ventilating System for 
Foundry with Unobstructed Craneway. 

From the ducts, discharge pipes are dropped at intervals of from 30 to 
40 feet. These usually terminate about 8 feet above the floor hne, and 
leave the ducts at an angle of about 45°, inclined in the direction of the 



582 Water Supply, Lighting, Heating and Ventilation 

air currents. Where the discharges are dropped as above stated, the 
open ends should incline about 20° from the vertical; they should 
alternately face the walls and the center bay. Six square inches of dis- 
charge opening are ordinarily allowed for every 1000 cubic feet of space, 
and the aggregate area of the openings should be 25 per cent greater 
than the area of the ducts. From these data the size of the ducts may 
be calculated for any building of known dimensions. 

Underground ducts with vertical discharge pipes are desirable, as 
they offer no obstruction to foundry operations, but they are quite 
expensive; the overhead ducts seem best to meet all requirements. 

Where steam or hot air is used for heating, the matter of ventilation 
requires no provision, except for that period of the day occupied in 
melting, as the leakages are sufficient to supply an abundance of fresh 
air. During the heat, vapor and gases rise in great volumes; to permit 
them to escape or to permit fresh air to enter, the swiveled windows in 
the monitor are opened. 

Where steam heat is employed, discomfort is occasionally experienced 
during cold or stormy weather, as the gases fall as soon as they begin 
to cool, and the vapor is condensed by the incoming air. With the hot- 
blast system this difficulty does not occur, since the plenum is sufficient 
to drive out the gases and vapor through the open windows. Mr. W. 
H. Carrier of the Buffalo Forge Company, Buffalo, N. Y., has discussed 
the subject of Foundry Heating and Ventilating so fully in a paper pre- 
sented at a meeting of the American Foundrymen's Association, that 
advantage is taken of the opportimity presented through the courtesy 
of the Buffalo Forge Company to make extensive extracts therefrom: 
"The proper distribution of heat in the foundry is comparatively difficult. 
In general the problem is that of a large open space, affording little 
opportunity for efficient placing of direct radiation. On account of 
the monitor type of building usually employed, there is relatively a 
great height. The hot air rises up into the lantern and passes out through 
the ventilators, if fans are not provided to deliver it near the floor. The 
heated column of air in the building serves to draw cold air from with- 
out at every opening. This inward leakage of cold air, not only de- 
mands a great amount of heat, but makes a thorough distribution of 
heat at the floor line most essential for comfort and economy of opera- 
tion. A slight plenum, or outward leakage, of air at the doors and 
openings, caused by the delivery and proper distribution of sufficient 
heated air into the building is the only solution of the difficulty. Ample 
ventilation is at times most necessary. The lantern t3^e of build- 
ing is best adapted to quickly ventilate, since the ventilators simply 
have to be opened to permit the hotter and lighter gases and vapors 



Heating and Ventilating 583 

to pass out. External air must enter the building to replace that 
escaping through the ventilators. Cold air entering the doors and 
openings tends to cool and condense the rising vapors. It is there- 
fore essential that a system be installed which will deliver warmed 
fresh air during the pouring periods, when ventilation is of first im- 
portance. 

Rapid heating of the building in the morning means that the best 
efficiency from the men will be obtained over the entire working period. 
A system which is elastic, and which may be rapidly varied to suit the 
requirements is to be favored. Coke or gas fired salamanders are appar- 
ently the most economical means of heating, as all the heat goes directly 
into the building. The atmosphere in a tightly closed building heated 
by this method becomes intolerable, and if sufficient ventilation is 
provided to make conditions healthful, the amount of heat required is 
greater than with other systems. The grade of fuel used is also con- 
siderably more expensive than that used in other systems of heating, 
to say nothing of the care of a large number of separate fires scattered 
about the building. 

In heating with direct radiation, steam is usually employed, although 
hot-water systems with forced circulation have been successfully oper- 
ated. Unless there is a large amount of hot water available, it is not 
an economical system to employ, on" account of the greatly increased 
amount of radiating surface required at the lower temperature. In 
steam heating, the high pressure, the low pressure or the vacuum system 
of distribution may be used; the selection of the particular system 
depends on load conditions. Where high-pressure steam is available, 
and there is no exhaust steam, it should of course, be used. If, however, 
there is no high pressure or exhaust steam available from the power 
plant, then an independent low-pressure boiler should be installed, fur- 
nishing steam at from 5 pounds to 10 pounds pressure. For low-pressure 
work cast-iron boilers may be used; no boiler feed pumps are required. 
The boiler should be placed at a level low enough for the condensation 
to drain back by gravity. If this is impracticable, then a centrifugal 
pump may be employed to return the condensed water to the boiler. 
A vacuum system should always be used when exhaust steam from the 
power plant is available. In a vacuum system of distribution, the 
back pressure should not exceed i pound, as otherwise the losses will 
outweigh the gain. The fan system is undoubtedly the best for foundry 
heating and ventilating, and it is particularly adapted to the severe 
requirements of foundries, and other buildings of this construction, 
where there are large open spaces to be heated. The principal advantages 
of the fan system over direct radiation are: 



584 Water Supply, Lighting, Heating and Ventilation 

1. The thorough distribution of heat secured by discharging the air 
under pressure through suitable outlets, with sufl&cient velocity to 
carry the heat to the points where it is most needed without causing 
perceptible draughts. 

2. No heat is wasted as in direct radiation, where a large part is sent 
directly through the walls, with slight effect upon the temperature of 
the building. The fan system affords means of supplying heat directly 
to the interior of the building. 

3. No heat is wasted by heating unoccupied spaces, as along the roof 
and in the monitor. Tests of the fan system installed in foundries have, 
in certain instances, shown lower temperatures in the monitors than at 
5 feet above the floor hne. 

4. Fan systems heat up very much more rapidly in the morning, 
when it is desirable to bring up the temperature in as short time as 
possible. 

5. It gives a rapid warm air change, which effectually removes 
smoke, steam and dust during pouring time; an effect possible only 
with a fan system. During such periods, when ventilation is required, 
the fresh and return air dampers should be adjusted to take all the air 
from out of doors. During the remainder of the day, however, the 
greater part of the air should be returned from the building to the 
apparatus, so that the heat required for ventilation may be the least 
possible. Precaution should always be taken to see that this feature 
is provided for. 

6. Fan systems cost less to install properly, since the apparatus is 
centrally located, and it is not necessary to pipe the steam to all parts 
of the building as in direct radiation. 

7. The cost of maintenance is less, since the radiating surface of a 
direct system along the walls is frequently damaged, while in the cen- 
trally-located fan apparatus, it is thoroughly protected. 

As in direct radiation, steam or hot water can be used in the fan 
system heater coils; but as the cool air is drawn over these coils by 
the fan, a great deal more heat is obtained from the same amount of 
heating surface. This permits the square feet of radiation to be re- 
duced about two-thirds. The fan is often driven by a direct-connected 
steam engine, the exhaust from which is used in the heater coils. This 
is an exceedingly economical method, as practically all of the heat of 
the steam is utilized. 

A new type of fan heating system, which is giving the highest degree 
of satisfaction, has been developed by the Buffalo Forge Company; this 
is the direct air furnace system. Instead of burning 'fuel under boilers , 
generating steam, transferring steam from boilers to heater coils through 



Heating and Ventilating 585 

a long run of pipe, and finally giving up heat to air from the heater 
coils, this system transfers the heat of the burning fuel directly to the 
air for distribution. An efficiency of 85 to 90 per cent has actually 
been attained, as against the usual efficiency of 50 to 60 per cent derived 
from steam service. The Buffalo Forge Company has made many 
installations using gas for fuel, and recently erected one in which pow- 
dered coal was used. Fuel oil can also be employed. The construc- 
tion of the furnace is similar to that for a water tube boiler. The hot 
gasses pass through the tubes, a fan draws the circulating air around 
the tubes, by which it is heated, and then distributes it through the 
building. Fig. 244 shows one of these furnaces recently installed in an 
important factory in the West. The main hot air ducts from the fan 
are usually made of galvanized iron, and are carried in the roof trusses. 
When these ducts are placed at a height not exceeding 20 feet, the air 
may be delivered directly into the building through short outlets. The 
design of these outlets is of particular importance to the success of the 
system. The velocity must be properly proportioned to the height, 
to the size of the outlet and to the horizontal distance which the air 
is to be blown. The greater the distance and height above the floor, 
and the smaller the outlets, the higher the velocity must be to obtain 
the proper distribution. On the other hand, if the velocity is exces- 
sive for these conditions, objectionable draughts will be produced. 

In some cases the main pipe has to be placed too far above the floor 
to permit good distribution of heat at the floor line with short outlets. 
In such cases it is usual to provide drop pipes from the main at the 
columns or along the side walls. Where the drop pipes are placed at 
the colunms, each pipe is usually provided with two branches; one 
blowing toward the base of the windows at the side walls, the other 
blowing toward the center of the building. Where the drop pipes are 
extended downward at the side walls, it is usual to provide three outlets 
to each pipe, two blowing sidewise along the walls, and the third out- 
ward toward the center of the building. 

In wide buildings it is customary to run two lines of pipes along the 
columns on each side; while in narrower buildings it is possible to 
obtain an entirely satisfactory distribution of heat with one line of 
main pipe, having outlets so proportioned as to blow across the building 
to the further side. A very neat, though more expensive system of 
distribution is with underground main ducts, with galvanized iron 
vertical risers, arranged along the columns or side walls; or in some 
instances, as in particularly wide buildings, at both places. The system 
of outlets in this case will be practically the same as where drop pipes 
are used. Fans may be either motor or engine driven. When an 



5S6 Water Supply, Lighting, Heating and Ventilation 

abundance of exhaust steam is available for use in the heater coils, the 
motor-driven fan will be found the more economical and satisfactory. It 
is preferred by many on account of the simplicity of operation and the 
shght care and attention required. With small fans it is good practice 
to direct-connect the motor to the fan; but with the larger apparatus 
the speed of operation is so low as to make it advisable to belt-drive the 
fan, by reason of the high cost of slow speed motors. Engine -driven 
fans are advisable when moderately high pressure steam is available. 
The steam can be used to drive the fan and the exhaust is available for 
the heater coils. This method is exceedingly economical, since prac- 
tically all of the heat is utihzed. 

The power used to drive the fan is almost negligible, as the engine is 
really little more than a pressure reducing valve. The speed of operation 
with engine drive is also much more flexible, allowing a wider range of 
speed, as may be necessitated by varying weather conditions. Direct 
radiation and the fan system of heating cost practically the same to 
install, the fan system as a rule being somewhat cheaper. Of course, 
with the fan system, the power necessary to drive the fan is additional, 
and it might seem that the operating expense would be somewhat more 
than with direct radiation ; but the more equable distribution of heat by 
the fan system cuts down the losses and reduces the radiating surface 
materially. The operating expenses of the two systems, however, vary 
little in the long run. " 



CHAPTER XXVII 
FOUNDRY ACCOUNTS 

Any system of foundry accounting must be subject to variation in 
details to meet the requirements of different classes of work. 

A system suitable for a foundry producing pipe, car wheels or other 
standard work must be modified in some of its details to adapt it to 
the requirements of a jobbing foundry. The value of an accounting 
system, aside from determining the cost of production, Ues in r-educing 
the expenses and in pointing out by comparative analysis the direction 
in which reductions can be made. 

Cost keeping is too often neglected. Many foundrymen establishing 
prices, etc., by those of competitors, have absolutely no knowledge of 
actual costs. There are few branches of business in which the indirect 
expenses, those apart from the cost of material and labor, exceed those 
of the foundry. Only by constant comparison, by tracing increase or 
decrease from one period to another, and continually following lines 
indicating improved results, can the expenses be made to approach the 
minimum. 

An effective cost system must not only furnish accurate results, but 
must furnish them promptly, so as to permit ready and periodical com- 
parison. 

Prompt information as to any means of increasing production or of 
decreasing losses or costs greatly enhances its value. The system must 
not be so elaborate as to render it impractical, but simplicity must not 
be accompanied with neglect. One that is not accurately or system- 
atically followed is worse than useless. Any effective system requires a 
large amount of clerical work, but the results are profitable in the high- 
est degree. 

The one given below has been in satisfactory use by a large manu- 
facturing establishment, making castings for its own consimaption. 

An order emanates from the management, going to the drawing room. 
There it is given a shop order number. A form bearing this number is 
filled out, showing the patterns required, the drawing number, pattern 
number and number of castings wanted from each pattern, date of 
delivery from the foundry and any changes to be made. This form, 
No. I, passes to the Requisition Clerk, who makes a requisition in quad- 

587 



588 



Foundry Accounts 



ruple, form No. 2, on the foundry. This form is about six by nine inches; 
and as many sets of blanks, all bearing the same shop order number, are 
used as are required. These forms are in shape for indexing with 
guide cards. Three of each set of these forms after completion are 
sent to the foundry, and the fourth is filed in the office. 

Of the three sets sent to the foundry, one is marked "Foundry Requisi- 
tion," one "Pattern Shop" and the third "Core Room." 

The foundry clerk fills in date of receipt, date for delivery of patterns 
and cores and the casting date; then, having marked on them the 
deUveries required, he transmits to the Pattern Shop and Core Room 
their respective requisitions. The Pattern Shop and Core Room fore- 
men each stamp them with date of receipt. 



Form 2. 



FOUNDRY REQUISITION 

Williams & Jones 



Shop Order, 5486. Date, 3/9/10. Castings wanted, 4/4/10. 

For 25 9x12 C. Crank, S. Valve Throttling Engines. 



Name of part 


Drawing 
number 


Pattern 
number 


No. of 
pieces 
wanted 


Alterations 


Cylinder 


7984 

8092 
8093 
8140 
8098 

8099 
7642 
7990 
7991 


46,854 

46,855 
46,856 
46,857 
46,859 

46,860 
46,861 
46,862 
46,863 


25 

25 

25 

25 
25 

25 

100 

25 

8 


Increase thickness of 


Front head 


flange at exhaust out- 
let Vs inch. 


Back head 




St'f'ng box gland 

Steam chest cover 

Steam chest glands 

Cylinder lagging 

Piston 


Add He inch to each end 
of cover. 











Requisition received in foundry, 3/ 10/10. 
Requisition received in pattern shop. 
Requisition received in core room. 



Order to be completed, 3/31/10.* 
Floor date, 3/22/10. 
Patterns wanted, 3/21/10. 
Cores wanted, four sets, 3/22/10. 
Four sets each day thereafter. 











Record of Castings Made 










Date 


Good 


Bad 


Date 


Good 


Bad 


Date 


Good 


Bad 


Date 


Good 


Bad 


3/22 


3 


I 


3/29 


2 
















3/23 


4 






















3/24 


4 






















3/25 


4 






















3/26 


4 






















3/28 


4 























Pattern Card 



589 



In filling out the floor or casting date, the date of delivery, etc., the 
foundry clerk knows that only four cyUnders can be made at each heat. 
He therefore fixes the date for completion at 3/31/ 10; this allows four 
days to provide for any contingencies. The Foundry Requisition is 
then filed under its floor date." 

At the end of each week the index cards up to that date are with- 
drawn from the front and passed to rear of card box. There are enough 
cards in the box to cover six months or a year as desired. 

Any unfilled orders at the end of the week are advanced to the first 
date of the coming week, so that the current orders are aU at the front 
of the box. Each day the foreman and clerk spend time to select 
orders and make out a program for the next heat. 

As the orders are completed, each requisition with its supplementary 
orders is filed away for reference. 

The Foundry Pattern Loft is divided into two parts, one for uncom- 
pleted orders (Live End), and the other for completed orders (Dead 
End). 

The patterns are delivered by Pattern shop at the Live End. 

A man from Pattern Storage has a book in which he takes receipts 
for patterns delivered. He also receipts for patterns which he removes 
from Dead End. 

Precisely the same system is pursued with core boxes. The Pattern 
Shop delivers and removes the boxes, taking and giving receipts. 

Attached to each pattern is a tag, on which all the data above the 
heavy line is made out in Pattern Shop : all below is filled out in Foundry. 

PATTERN CARD 



o 





Moulder's Tag. 


Foundry Tag. 


F 


Date issued, 3/21/10. 


: Date issued, 3/21/10 ' 





Shop order, 5486. 


Shop order, 5486. 


r 


Name of piece, 9X12 cylinder. 


Name of piece, 9x12 cyUnder. 


m 


Pattern No. 46,854- 


Pattern No. 46,854. 


3 


No. wanted 25. Date 3/31. 


No. wanted 25, date, 3/31. 




Name of moulder, John Hayes. 


Name of moulder, John Hayes. 




Date in sand, 3/22/10. 


Date in sand, 3/22/10. 




Tally //// //// //// //// //// 


Moulder's time. 




Moulder must return this tag 


John Hayes - ¥ ¥ ¥ ¥ ¥ 




with pattern. 


John Hayes - V- ¥ ¥ 
Wm. Moran - ¥ ¥ ¥ ¥ ¥ 
Wm. Moran — %' ¥ ¥ 



The tag is perforated across the middle. When the pattern is issued 
to the moulder, the clerk tears off and retains the foundry tag on which 



590 



Foundry Accounts 



the time is entered and then filed away. The moulder's tag is de- 
stroyed when pattern is removed to storage. 

The foreman of core room enters time of core makers on core room 
requisition. It will be noticed that the clerk has not only entered on 
the Foundry tag the time of John Hayes, but also that of Wm. Moran, 
helper. 

There must be a case in which are kept cards showing records of pig 
iron, scrap, coke, sand, sea coal, fire clay and any other material re- 
ceived in car lots. 

PIG IRON CARD 



Car, N. P. R.R., 438,827 
Wt., G. T., 24.23. 



Pig Iron 
From Jones, Smith & Company 
Brand No. 2, S. 
A nalysis 



Received, 2/10/10. 
Price. $16.50 Did. 



Silicon 
2.38 



Sulphur 
.032 



Phosphorus 
.43 



Manganese 
• 54 



Net weight, 54,282. 
Expended, 54,660. 
Overrun, 378. 



o I 00 



o 6 o o lo o Q ! 
o, q o_ o^ 00.0 : 

IN 00" o" o" PJ rO ai 00 

00 M 1-1 1-1 

•^ :;;;:;; ' 

\r, 

-T) 

^ s ■ 

g) a ::::::: § 
JS » ^ 

. . ^-- "-- ~\ ~\ ^-- ^^ ^-^ X 

+j-(_>(NC»lNCqM(NN O 



On back of this card the withdrawals and corresponding dates are 
entered and balance cast up on face. 

The cards for sand, fire clay, etc., are the same as for coke, without 
the analysis. It is advisable, however, to have these supplies analyzed 
occasionally. 



Pig Iron 
COKE CARD 



591 



COICE 




Form 5. 




Car No. 7482, N. Y. C. 


Received, 2/7/10. 


Ovens, Hamilton by-product. 


Weight, 32,600. 


$4.85 Deld. 




Analysis 






Per cent 


Fixed carbon 


8s 


Sulphur 


8 


Ash : 


II 


Moisture 


T 


1 



As a matter of convenience to the foreman in making up the mixture, 
it is desirable to enter the pig iron in a special book, as per diagram 
below as well as to keep the cards. 



PIG IRON 



Form 6. 



Sample Page of Pig Iron Book. 



Date 

re- 
ceived 


Car 

No. 


Brand 


Net 
weight 


Ex- 
pended 


12/9/09 


132,568 


No. 2S 


78,594 


12/20 


12/9/09 


35.689 


No. 2S 


76,432 


12/27 


12/1S/09 


46,351 


No. 2 N 


69,496 


1/14/10 


1/7/10 


25,135 


No. 3N 


58,439 


2/8/10 


2/10/10 


439.827 


N0-2S 


54,282 


3/2/10 



Analysis 



I* Si 3.2s S .03 P .89 Mn .82 

2* Si 3.09 S .032 P .85 Mn .76 

1 Si 2.84 S .038 P .76 Mn .68 

2 Si 2.80 S .040 P .74 Mn .66 

1 Si 2.19 S .027 P .29 Mn .75 

2 Si 2.10 S .026 P .27 Mn .74 

1 Si 1.67 S .024 P .26 Mn .69 

2 Si 1.65 S .023 P .24 Mn .67 



.52 



1 Si 2.38 S .032 P .43 Mn .54 

2 Si 2.2s S .036 P .48 Mn 



* No. I is the furnace analysis; No. 2, that of the foundry chemist. 

The Heat Book is given on page 592. In this book the foreman enters 
for the coming heat the irons which are to be used and the mixture. 
The remainder of the account may be filled out later by the clerk after 
returns are made. This book is of the greatest importance as it enables 



592 



Foundry Accounts 



the foreman to repeat at once any mixture used at any time, or for any 
particular purpose. 

The sheet shown is for the heat of 2/22/ from which 4 cyUnders are 
to be poured and a special charge (the first) containing 10 per cent steel 
scrap is made. The cylinders weigh about 500 pounds each, and as 
there are crank disc and other castings requiring strong iron, the entire 
first charge will contain steel. 

The charges are 4000 pounds each, and the mixture is uniform through- 
out the heat, except for first and last charges. Turning to the Pig Iron 
Book, the foreman selects such iron as will furnish the desired mixture 
for cylinders, also those for the remaining charges and enters them on 
the heat book. A memorandum is given the boss of the yard gang, 
showing the car numbers and the amount of iron from each car for each 
charge. 

The number of charges for the ordinary mixture is left blank until 
later in the day, when the total amount to be melted is ascertained. 

The weighman has a pad of forms upon which he prepares a slip for 
each charge giving the car number, weight of iron from each car, weight 
of coke and lime. 

Each charge of iron is piled by itself on cupola platform in regular 
order. The coke with limestone is sent up in cars as the charging of 
cupola proceeds. 



SAMPLE SHEET FROM HEAT BOOK 

Williams & Jones Foundry 



Form 7. 
















Heat of 3/22/10. 






Weight 


















Pig iron 


Car 
No. 


per 
charge. 


No. of 
charges 




Analysis 






Remarks 






pounds 


















Silvery 


8.296 


200' 




Si 4.20 S 


.03 


P 


.72 


Mn 


.68 




No. 2 Sou . 


439,827 


400 




Si 2.25 S 


.036 


P 


.48 


Mn 


• 52 




No. 2 Sou. . 


46,351 


400 




Si 2.10 S 


.026 


P 


.27 


Mn 


.74 


First 


No. 2 Nor.. 


328,503 


800 • 


I 


Si 2.29 S 


.023 


P 


.24 


Mn 


.67 


charge 


No. 2 Nor.. 






















Scrap 




1800 




Si 2.10 S 


.084 


P 


.63 


Mn 


.63 




Steel scrap . 




400. 


















No. 2 Sou. . 


27,935 


800^ 




Si 3.75 S 


.017 


P 


.86 


Mn 


.36 




No. 2 Nor.. 


328,503 


600 




Si 2.29 S 


.023 


P 


.24 


Mn 


.67 


20 


No. 2 Nor.. 


45,541 


200 


20 


Si 1.92 S 


.024 


P 


.28 


Mn 


.63 


charges 


Scrap 




2400 




Si 2.10 S 


.084 


P 


.68 


Mn 


.63 


Last 


Clean-up . . . 




1050 


I 














charge 



Sample Sheet From Heat Book 



593 



Amount Charged 



Pig iron. 






33.800 


Scrap. 






49,800 


Steel scrap. 






400 


Clean-up. 






1,050 


Total. 






85,050 


Coke. 


10,950. 


Returned 320. 


10,630 


Fhix. 






1,600 



Production 



Good castings. 




66,466 


Bad castings. 




2,708 


Gates and sprues. 




6,106 


Over iron. 




5. 143 


Shot. 




650 


Clean-up. 




1,670 


Total accounted for. 




82,743 


Lost in melt. 




2,307 


Per cent melt in good castings. 




78.2 


Per cent castings good. 




96.1 


Per cent castings bad. 




3.9 


Per cent melt in returns. 




19.0 


Per cent loss in melt. 




2.7 


Iron melted per pound coke. 




8 lbs. to I 



Mixtures 



1st charge special. 
Regular charges. 



5% car 8296. 
20% car 328,503. 
20% car 27,935. 
60% scrap. 



10% car 439,827. 

10% steel. 

15% car 328,503. 



10% car 46,351. 
45% scrap. 
5% car 45,541. 



Analysis 



Computed. 


1st charge. 


Si 1.66 


S 


.075 


p 


.42 


Mn 


.46 


Have 


analyses 


Computed. 


Regular. 


Si 2.21 


S 


.088 


p 


.63 


Mn 


.47 


made 


as re- 


Actual. 


1st charge. 


Si 1.64 


s 


.080 


p 


.43 


Mn 


.45 


quired 




Actual. 


Regular. 


Si 2.23 


s 


.092 


p 


.65 


Mn 


• 44 







594 



Foundry Accounts 

Cost of Labor 





Productive 


Non- 
productive 


Totals 


Gen. 

Av. 




Hours 


Cost 


Hours 


Cost 


Hours 


Cost 


Cost 
per 
hour 


Foundry 

Core room 

Cleaning room 


I 133- 6 
II3-6 


$274.90 
34.08 


180 
36 
234 


S28.80 

5.76 

39-84 


1697.2 


$383.38 


22.60 


Total 


1247.2 


$308.98 


450 


$74.20 



Helpers are 
included in 
foundry as 
productive. 



Blast on, i :5o p.m. 
First tap, 2:15 p.m. 
Test bar special. 
Test bar regular. 



Pressure, 9 ounces. 
Bottom dropped, 4:45 p.m. 
Transverse, 2800. 
Transverse, 2200. 



First iron, 2 p. 



The melter and boss of the yard gang are each furnished with a copy 
of charging schedule. After the charges are all up, the weighman turns 
in to foundry office, slips for the bottom coke, and one for each charge 
giving complete weights of everything entering the cupola. 



Form 9. 



Charging Schedule 



Date, 3/22/10. 



Charges 



1st charge . 



20 charges . 



Last charge . 



Materials 



Bottom coke 

Steel scrap 

Car 8296 

Car 439.827 

Car 46,351 

Car 328,503 

Scrap (selected) 

Coke 

Car 27,935 

Car 328,503 

Car 45.541 

Scrap .' . . . 

Returned coke 

Clean-up 

Use 80 pounds limestone from third to 
nineteenth charge inclusive. 



Weights 



2850 
400 
200 
400 
400 
800 

1800 

400 
800 
600 
200 
2400 

100 
1050 



Weigh Slips 



595 



Form lo. 
Charge No. i. 


Weigh Ticket 


Date 


3/22/10. 


Coke bottom 






2850 
400 
200 
400 
400 
. 800 
1800 


Steel scrap , 






Car 8296 






Car 439,827 












Car 328,503 






Scrap 












Limestone. 



Form 10. 
Charge No. 2. 


Weigh Ticket 


Date, 3/23/10. 


Coke. . . 




400 


Car 27 935 




800 


Car 328,503 




600 


Car 45,541 . . ' 




200 


Scrap 




2400 1 




Limestone. 



On the day following the heat, after recovering the iron from the 
gangways, cinders, etc., the yard foreman turns the weight into the 
office. 



Form II. 
3/23/10. 


Returns 


FROM 


Foundry 


Heat of 3/22/10. 










650 












Shot 








650 


Clean-up 








1670 


Returned coke 








^20 


" 



The bad castings on above slip are those thrown out in the foundry, 
to which are subsequently added those rejected in the cleaning room. 



596 Foundry Accounts 

From the moulder's tags, turned in on the 22nd, and from information 
obtained from the floor concerning work on tags which have not been 
turned in, the clerk prepares in part, duphcate cleaning room reports. 
He enters the shop order numbers, pattern numbers, names of parts 
and nmnber of parts made. This report then goes to foreman of clean- 
ing room, who completes it, sending one copy to the foundry ofl&ce and 
the other to the work's office. 

The form is given on page 597. As many sheets as are necessary are 
used for each heat. 

The Time Book, Weigh Tickets, Foundry Returns and Cleaning Room 
Report furnish all the data, except analysis and test, for completion 
of entry in heat book for 3 22 10. Information as to the last two items 
is obtained from time to time as required. The heat report is made out 
in duplicate; original sent to Works Office and duplicate filed in Foundry. 
This is followed by a weekly summary. At the end of each month an 
inventory is taken of all supplies; and their cost, per himdred poimds 
good castings, is determined for the month passed. This cost is used in 
making out foundry reports for the succeeding month. 

All supplies except the btilky materials, such as sand, fire clay, etc. 
are kept in store room and are issued upon requisition from foremen 
or clerk, upon blanks as per sketch. 



Requisition on Dale, 3/21/10. 

Store Keeper, Issue to 

Jno. Sullivan, 
5 Pounds Silver Lead. 

Wm. Wilson, Foreman. 



These requisitions, together with tallies of sand, fire clay, etc., are 
turned into office by store keeper at end of month. 

Careful scrutiny and comparison of these monthly statements and 
expenditures result in marked savings. They promote among the 
departments a strife for the lowest record. The reduction in the amount 
of core supplies, nails, rods and sand is especially noticeable. 

As regards iron flasks and other castings made for the foundry, if 
they are for permanent equipment, they are so charged. If on the 
other hand they are for temporary ser\dce, they are charged to foundry 
at cost of labor, plus the difference between the cost of good castings 
and scrap. 

Monthly comparisons, or more frequent if desired, are made with 
statements from the works office. Comparisons are likewise made at 
the end of the fiscal year. 



Cleaning Room Report 



597 



TO T) 



rONTfON'^NO 



00 O^ O* ro M ro 00 ^ 



S.6 



rOM-*fON-*CN|VOH 



fJN-^fVjeqrtCStOW 






o aj w ij w ^ :=; 



,<^ 



&; &h" o 0^ ►^ p^ 



M i-i w O O O 
M (M <N (N (N N 






P! N <N <N CS CM 



.S a Ti<s ^ ,^ ,^ "1 o o 

OfeCQOTCOWOPnP^ 



^ O 
CM 







00 


=0. 


00 






*- 
"§ 


«5 


to 


1 


lO 


1 


§ 
s 


s 
s 


s 

^ 


lO 


1 






598 



Foundry Accounts 



Form 14. 



FOUNDRY 

Williams & 
Heat of 



Grade 


No. I 




No. 2 




No. 3 




No. 4 






Car No. 

Silvery 

8296 


Weight 
200 


Car No. 
Sou. 

439,827 
46,351 
27,935 


Weight 

No. 2 N.^ 

400 

400 

16,000 


Car No. 

328,503 
45,541 


Weight 

12,800 
4,000 


Car No. 


Weight 


Weight... 
Cost 




200 
$1.49 




16,800 
S123.73 




16,800 
$127.51 





















_^ 






"rtij 


-S.r- 




Returns not 
including 

bad 
castings 


■S^ 


•0 


'1.1 


'^0 




H 


Cost 

Iron 

goo 

casti 





J6 


8° 


|1^ 


Weight... 


85.050 


66,466 


2708 


13,569 


2307 


82,743 


78.2 


96.1 


Cost 


$634.66 


$520.73 















Costs 















to 


w 


>. to 












w M 


h OT M 


W M 


H m M 




c 

1 




> 

^1 


3 
e2 


ill 




III 


'-'00 


otal found 

cost per 
100 pound 
ood castin 




























M 


'^'' M 


M 


H M 


Hours 


1133-6 


113. 6 


450 


1697.2 


2.55 








Cost 


$274.98 


$34.08 


$74.40 


$383.38 


$0.5765 


$0,0396 


$0,783 


$1,399 



Foundry Reports 



599 



REPORTS 

Jones Co. 
3/22/10. 

















CO a 








to 








^.13 


iH-o 




— 0. 

11 


^1= p. 


1 

.2" 










IP 


^§1 


















400 


49,800 


loso 


85,050 


10,630 


1600 


8-1 






$3.00 


$348.60 


$4.20 


S608.53 


$25.53 


So. 60 




$0,746 








3.9 



ga 






Total cost of melt . . 
Cr. 

Returns 16,275 pounds 
.70 



Cost of iron in good 
casting 



$634.66 
113.93 


III 


520.73 




$0,783 



6oo 



Foundry Accounts 
WEEKLY FOUNDRY REPORT 

Williams & Jones Foundry 



Form IS 


• 














Heats of 3/23-2S and 28/10. 


Date 








of 




Consumption 


Product 


heat 








u 


"a 


"2 

6-- 


0. 

2 


t. 





1 


3 


-si 




1^1 


|| 


1 


1 


^•S 


^•S 


c^ 


!/3 


H 





fe 


0^ 



M| 


-^^ 
(4-^^ 


h 


23 


36,500 


5,800 


32,980 


5.000 


80,360 


11,250 


1250 


57,859 


2703 


16,172 


3626 


80,360 


25 


27,720 


3.600 


23,880 


5.000 


60,200 


9.540 


900 


43,344 


1340 


13,244 


2272 


60,200 


28 


27,520 


7,800 


26,800 




62,200 


9.930 


950 


45.406 


1900 


12,406 


2488 


62,200 


Totals.. 


91.740 


17,280 


83.740 


10,000 


202,760 


30,720 


3100 


146,609 


5943 


41,822 


8386 


202,760 



Summary 



Total iron melted 

Total coke used 

Total flux used 

Total cost melt 

Credit 

Returns (including bad castings) 7oj^ per 100 pounds 

Total loss 

Total good castings 

Total bad castings 



Total productive labor 

Total non-productive labor 

Total labor 

Total cost of supplies 

Total foundry cost of good castings . 



Per cent of melt in good castings 

Per cent of melt in bad castings 

Per cent of melt in bad return (including bad cast- 
ings) 

Per cent of melt in loss 

Per cent of castings good 

Per cent of castings bad 



Average cost of labor per hour 

Cost of iron per 100 pounds 

Cost of iron melted per 100 pounds 

Cost of iron in good castings oer 100 pounds 

Cost of labor, good castings per 100 pounds 

Cost of supplies, good castings per 100 pounds 

Total foundry cost, good castings per 100 pounds . 
Iron melted per pound of coke 



Pounds 

20,7260 

30,720 

3,100 



47,765 

8,386 

146,609 

5.943 

Hours 
2,482 
1,490 
3.972 



6.6 lbs. 



$1476.09 

74.50 

1. 17 

1551.76 

33460 



615.72 
246.29 



Per cent 
72.3 
2.93 

23.5 
4-1 

96.1 

3.9 

Cents 

21.7 
0.728 
0.76s 



1217.16 



826.01 

58.05 

2137.22 



0.830 
0.588 
0.0396 
1.4576 



Monthly Expenditure of Supplies 



6oi 



Form i6. 



MONTHLY EXPENDITURE OF SUPPLIES 

Williams & Jones Foundry 

February, 1910. 



Materials 



Quantity 



OS 



o ^ 



Anchors 

Belting 

Belt lacing 

Bellows 

Beeswax 

Bolts 

Brick, red 

Brick, fire 

Brick, block 

Brooms 

Barrows, wheel 

Barrows, pig iron 

Brushes, soft 

Brushes, hard 

Brushes, core 

Brushes, casting 

Brushes, camel's hair. . . 

Brushes, paint . '. 

Brushes, white wash. . . 

Brushes, wheel 

Blocks, chain 

Candles 

Cable wire 

Carbons , 

Castings 

Cans, blow 

Chisels, cold 

Chaplets 

Charcoal 

Chain 

Chain links 

Chalk 

Chalk, line 

Clay 

Clay, fire 

Clamps 

Clamps, spike 

Clamps, screw 

Core, compound dry. . . 
Core, compound liquid 

Core vent, metallic 

Coke forks 

Coke baskets 



6o2 Foundry Accounts 

Monthly Expenditure of Supplies (Continued) 



Materials 



Quantity 



3s 






3 O 



Coke scoops 

Crow bars 

Crucibles 

Cloth wire ...;... 

Cups, tin 

Cutter's emery. . . 
Facing mineral... 

Flour 

Fuel 

Gauges, wind 

Gauges, air 

Globes, electric . . . 
Globes, lantern. . . 

Glue 

Glutrin 

Grease 

Hammers 

Handles, hammer 
Handles, sledge... 

Hose, air 

Hose, water 

Hose, couplings . . 

Hose, nozzles 

Iron bar 

Iron, sheet 

Irons, draw 

Irons, flasks 

Jackscrew 

Jack-bolts 

Levels, spirit 

Lead, bar 

Lead, sheet 

Lead, pipe 

Lead, red 

Lead, white 

Lead, silver 

Lime 

Lumber 

Litharge 

Lycopodium 

Mallets 

Mauls 



Monthly Expenditure of Supplies 
Monthly Expenditure of Supplies (Continued) 



603 



Materials 



Manganese, ferro 

Mercury 

Molasses 

Nails 

Nuts 

Oil, core 

Oil, coal 

Oil, belt 

Oil, lard...." 

Oil, linseed 

Oil, hard 

Oil, black 

Oil, machine .... 

Oil, rosin 

Oil, cans 

Pails, iron 

Pails, wood 

Pencils, lead. . . . 

Pipe, iron 

Pipe, fittings 

Picks, cupola 

Pliers 

Pliers, cutting... 
Pots, sprinkling. 

Paper, sand 

Paper, toilet 

Paper, emery 

Paper, wrapping. 

Rammers 

Rammers, bench 

Riddles 

Riddles, brass 

Rivets, copper... 

Rivets, iron 

Rosin 

Rope 

Saws, hand 

Saws, hack 

Screws 

xScrews, drivers . . . 

Stationary 

Scrapers - 

Silicon, ferro 

Straps, lifting. . . , 
Stars, tumbler. . . 
Sand, moulding , 



Quantity 



OS 






■-BB 



6o4 Foundry Accounts 

Monthly Expenditure of Supplies (Continued) 



Materials 



Quantity 



2S 
o o 

^2 



•S6 



a o 

o ^ 



H 



Sand, lake 

Sand, bank 

Sand, fire 

Shovels, moulders' 
Shovels, laborers' . , 
Sprayers, blacking. 

Sponges 

Smooth-on 

Swabs , 

Sledges 

Stone, emery 

Salt 

Sulphur 

Sea coal 

Talc 

Tacks 

Torches, blow 

Twine 

Straw 

Vitriol 

Wire, iron 

Wire, copper 

Wire, wax vent 

Wire, cable 

Washers 

Wheels, emery 

Wheels, sheave 

Wheels, barrow 

Wrenches, open 

Wrenches, monkey. 
Wrenches, pipe 



Total $284.56 

Good castings for month 7X8.57- 

Cost of supplies for 100 good castings for February, 1910 $0.0396 

Use this price for the month of March, 1910. 



Monthly Comparisons of Foundry Accounts 



605 



O ^ 

SI 

g g 



o g 

S § 

<! 2 

i i 

S I 

§ s 




fO t- o 

M t~ 00 
«0 00 t^ 





ioOOOnOI>0 >/5 








s 


^ 


S 


^^ 8 


^ 


t~ 1/5 rfoo '^ 




ro 


" 



O cd 
O 



2 S^ 6 



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Foundry Accounts 






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Monthly Comparison of Foundry Accounts 



607 






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Annual Comparison of Foundry Accounts 



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Transmission of Orders 



6ii 



Chart Showing Direction or Transmission of Shop and 
Foundry Orders, Together With That of Return 
Reports 



1 j Superintendent 



Drawing Room 



Works Office 




Cleanincj Yard 
Room 



Cupola Moulding 



Floor 







Core 
Room 



Fig. 245. 



The chart above shows the direction of transmission of orders from 
the superintendent to the foundry office, and thence, with supplementary 
orders, to the dehvery of the completed product at the cleaning room; 
as also that of return reports to foundry office, works office, and superin- 
tendent. Full lines indicate the course of orders outward; dotted lines 
that of the return reports. 



From Superintendent . 



From Drawing Room . 



From Foundry. 



From Foundry Office. 



(i) to 



(2) to 



(4) to 



(4) to 



Works Office . . . 
Drawing Room. 

Foundry 

Works Office . . . 
Pattern Shop . . 
Pattern Shop . . 
Core Room. . . . 

Floor 

Cupola 

Yard 

Cleaning Room . 



(3) 

(2) 

(4) 

(3) 

(5) 

(5) 

(6) 

(7) 

■ (8) 

. (9) 

(10) 



6 12 Foundry Accounts 

From Pattern Shop (5) to | IZtL^''/. ! i : ! '(^ 

From Core Room (6) to Moulding Floor (7) 

From Cupola (8) to Moulding Floor .... (7) 

From Moulding Floor (7) to Cleaning Room. ... (10) 

Return Reports 

From Moulding Floor. ... (y)^ 

From Core Room (6) > r:, •, ^^c / x 

FromCupola ..: (8) ^^ Foundry Office (4) 

From Cleaning Room. . . .(io)J 

From Foundry Office (4) to {'^^S"^^^':.::: S 

From Works Office (3) to Superintendent (i) 

The system of accounting as above described has been followed for 
some years by one of the western foundries, with excellent results. It 
involves considerable clerical work, but one clerk can handle it. 

Some modifications are required to adapt it to a jobbing foundry. 
These are indicated at once and are readily made. 

As showing different methods of foundry accounting, each having its 
advantages and disadvantages, papers presented on the subject to the 
American Foundrymen's Association by Mr. B. A. FrankHn and Mr. J. 
P. Golden are given. . . One can be developed from the lot which will 
meet any requirement. 



AMERICAN FOUNDRYMEN'S ASSOCIATION 

Foundry Costs 
By B. a. Franklin, Boston, Mass. 
"... Form I illustrates the first method of foundry cost showing: 
The operations are divided into the elements of^ 

Section A 



Melting, 



Moulding 



Metal. 2. Fuel. 

3. Melting Expense. 

Section B 



4. Moulding Labor. 
5. Moulding Expense — Floor and Bench separately 

Section C 

6. Cleaning Labor. 10. Pickling. 

7. Cleaning Expense. 11. Pickling Expense. 

8. Tumbling Labor. 12. Sand Blasting Labor. 

9. TumbUng Expense. 13. Sand Blasting Expense. 



Foundry Costs 613 

Section D 
14. Core Labor. 15. Core Expense. 

Section E 
16. General Expense. 

"In discussing this system no attempt is made to discuss the method 
of getting the information because such methods are simple and easily 
worked out." 

"The Basic Costs are illustrated in Form i, which shows the weekly 
operation of the foundry as a whole, and Form 2 represents the cost of 
an actual casting. Form 3 represents the monthly foundry showing 
of profit and loss, ofifering means of proof of the foundry cost and show- 
ing the net result. " 

". . . As nearly as possible foundry shop economy demands, and 
foundry work permits a daily clean-up, though, of course, some oper- 
ations happen one day after the beginning." 

"A foundry cost might then be a daily record sheet. ' Weekly records, 
however, are sufi&cient generally, and the one presented is on this 
basis. " 

Form i 

^'Section A. Deals with metal." 

"Here is shown, separately for each different mixture, of which one 
foundry might generally employ two or three, the weights and value 
of iron charged. These weights may readily be proved by checking 
as each car or lot of scrap is used up. In the case of scrap made in the 
foundry or 'own scrap' no value is put on -this since it' is put into the 
heat in an iron foundry, on the basis that scrap made on each heat will 
be approximately the same per cent, and what is made one day is gathered 
up and used the next day. The exception to this is in the case of 'bad 
castings,' charged at scrap value, and, as seen later, accounted for in 
casting cost." 

"In a Steel Foundry it would be necessary to change all scrap at 
scrap value and credit same to particular castings. " 

"The 'metal-used' value is shown and the pounds melted, 'but the 
'metal cost' is obtained by dividing, not by pounds melted, but by 
poimds of 'castings made' — i.e., good and bad castings. The bad 
castings are to be charged to the particular order as will be seen later. 
We thus arrive at a weekly metal cost for each mixture. " 

"Likewise for purposes 'of general guidance, there is shown weekly 
the 'per cent, of good castings to melt,' the 'per cent of bad castings 



6i4 Foundry Accounts 

to castings made,' and the per cent of metal disappearance or 'per cent 
of loss.' " 

"Now for management guidance toward general shop economy, 
these figures present standards and bases for striving for lower costs — 
viz., to make the percentage of good castings to the melt as high as 
possible, to make the percentage of bad castings to castings made as 
low as possible, and the record will quickly show that the cost fluctuates 
with these conditions." 

"And it will be found that melting and handling of metal and fuel 
can be done on piece work to bring best economy in metal-cost." 

"A definite and valuable point to note is that in addition to the 
weekly figure of cost per pound, there is carried along the average or 

'period cost per pound.' This is the figure to be used in cost work. 

J) 

"... The weekly figures are constantly compared with the period 
figures showing whether the weekly result is better or worse than the 
average, and an observation of the detail shows why. ..." 

" In each section it will be noted that the costs are brought down to a 
few vital units or percentages, and when these vary, they are significant 
of a gain or loss in economy of production, the reason for which can be 
readily observed by casting the eye up the details and observing the 
comparison of them." 

"... Section B. Moulding. — Here are two elements to be con- 
sidered — productive labor and expense. The expense is shown in 
relation to productive labor. It may be shown in relation to hours if 
desired, but in each class of moulding labor there is generally no great 
fluctuation of rate per hour. ..." 

"The productive labor and expense should be kept separately as to 
class of moulding, as floor, bench, machine, etc., since the expense varies 
considerably with the class." 

"... A little thought and experiment would seem to show that on 
the whole the expenses approximately vary according to time spent in 
productive labor rather than by the pound. " 

"In the matter of productive labor it is to be understood that 
money paid for moulding each job, whether day work or piece work, 
is to be known and used in figuring definite casting, as shown in 
Form 2." 

"It is in this productive labor cost that the first element of variation 
in casting costs is to be found, the expense percentage being the same or 
taken as the same, except in the matter of certain direct charges or 
expenses to be discussed later. " 



Foundry Costs 615 

"Section C. Cleaning Castings. — In the matter of cleaning castings 
there must be some division. Tiunbling, pickling, and sand blasting 
are taken separately as shown below. This leaves for consideration 
here the cleaning of castings by other than these three methods and 
applies mainly to large castings. ..." 

" . . . In Tumbling the labor can best be put on piece work and will 
generally be done by the pound, and expenses will be shown by the 
pound. ..." 

''In Sand Blasting and Pickling the expenses are shown in relation to 
productive labor, and the work can be put on piece work. ..." 

"Section D. Core Room. — Here the labor can in the main be put 
on f>iece work and the expenses shown in detail. ..." 

"Section E. . . . General Expenses. — This is shown in relation to 
productive labor, the items of productive labor being those of Moulding, 
Core Making and Cleaning operations. 

"... Thus we arrive at certain weekly and period basic figures of 
cost in the main elements in the foundry of 

Metal. Core Making. 

Moulding. General Expenses. 

Cleaning. 

"The items of metal and expense are easily provable with the books 
monthly, .and the labor with the pay roll weekly, so that we get a proved 
weekly picture of the foundry situation as compared with average or 
period, and we get it in such detail as will show the reasons of all varia- 
tions of operation. ..." 

"Consideration of Casting Cost. The first element to consider is 
that of direct charges. In many jobs, but by no means all of them, 
are certain charges which it seems desirable should be charged directly 
to the particular order. They need in most foundry work be very small 
in number. These charges must essentially be gathered and held until 
the job is shipped and cost ready to work out. " 

Form 2 

"Form 2 illustrates this final casting cost." 

"In all castings finished in a given period, the varying elements of 
unit cost would be purely the productive labor items of moulding and 
cleaning and direct charges, the metal, fuel, melting, moulding, cleaning 
and general expense charges being taken from the period figures on the 
weekly cost sheet." 

"Therefore, in working out the cost of a finished casting, it is essential 
to know of it as a particular job; the weight — and the shipping slip 



6i6 Foundry Accounts 

gives that; the moulding and core making labor and the cleaning labor, 
whefe average rates per pound are not used. " 

"... Direct charges are added and also loss on bad castings. A 
record of bad castings is necessary and simple." 

"On bad castings the loss would depend on how far the work had 
progressed when discovered as bad, and what work on them had been 
paid for. The metal, of course, would be credited at scrap value." 

"By this method then it will be observed that with very small clerical 
labor, the practical foundryman or manager gets a weekly, or daily, 
if he so designs, view of his foundry costs and their fluctuations which 
form a definite and correct basis for accurate estimate, and he can very 
quickly get a particular job or casting cost by having the money spent 
on moulding and cleaning, etc., gathered." 

"The Cost System settled, the bookkeeping should be made to parallel 
the cost system, in which case the monthly showing would be made to 
show as per Form 3." 

"Thus is obtained a complete monthly analysis. In most foundries 
one clerk and almost invariably two, can operate the system as far as 
costs are concerned." 



Cost of Metal 



617 



Metal — Section A. No. i. Form i 



Mixture No. i 

Pig Grade i 

Pig Grade 2 

Pig Grade 3 

Pig Grade 4 

Pig Grade 5 

Bought scrap 

"Own scrap chillers 

Own scrap floor scrap 

Own scrap bad castings 

Own scrap gates 

Weekly totals metal used 

Period totals metal used 

Weekly total pounds castings 

made 

Period total pounds castings 

made 

Good castings made 

Period castings made 

Per cent good castings to melt 
Period per cent castings made 

Bad castings 

Per cent bad castings to 

castings made 

Shop scrap 

Per cent shop scrap . 

Total pounds (weekly) 

Total pounds (period) . 

Pounds lost 

Period pounds lost 

Per cent lost 

Period per cent lost 

Weekly metal cost per 100 

pounds 

Period metal cost per 100 

pounds 



Oct. 9 



Pounds 



34,240 

32,270 

5,680 

36,310 

31,500 

15.900 

1,275 

7,300 

10,000 

36,100 

210,575 



149,280 

140,125 
66.5 
9,155 

6.1 
51,8c 

210,08 

9,495' 

4.5 



Amount 



252 . 22 
234-10 
38.67 
259.35 
249 . 61 
106.47 
o 



Oct. 16 



Pounds 



33,950 

33,290 

14,270 

32,070 

32,720 

17,000 

1,420 

9,000 

9,000 

34,800 

217,520 

428,095 

150,441 

299,721 
139.867 
279,992 
64 .3 

10,574 

7 
54,400 

204,841 

12,679 
22,174 
5.8 



.84 



Amount 



253.87 
249.68 
97. IS 
232.65 
259.28 
113.84 



63.00 
o 
1269.47 
2479.89 



Oct. 23 



Pounds 



25,620 

25,440 
6,010 

30,150 

25,' 

11,900 
1,135 
7,700 

10,000 

26,500 
169,535 
597,630 

116,^ 

416,172 
109,069 
389,061 

64.3 

65.1 
7,382 

6.3 

43,700 

160,151 

9,384 
31.558 
5.5 
5.3 

.85 

.83 



Amount 



191.58 
187.39 
40.92 
218,72 
198.74 
79.68 
o 
o 

70.00 
o 

987.03 

3466.92 



6i8 



Foundry Accounts 



Metal — Section A — No. 2. Form i 



Fuel and melting expense 

Labor (cupola men) 

Labor (handling coke and 
coal) 

Labor (miscellaneous) 

Labor (handling iron) 

Coke 

Coal 

Wood. 

Fire brick. 

Fire clay 

Oyster shells 

Mica sand 

Chg. from other depts. 

Analysis of iron 

Relining cupola and repairs. . 

Tumbling cupola bottom 

Crane labor 

Elevator labor 

Blower labor 

Handling oyster shells. 

Bituminous facing. 

Interest on investment 

Heat, light and power 

Taxes, insurance and depre- 
ciation 

Weekly expense 

Period expense 

Weekly pounds castings made 

Period pounds castings made. 

Weekly cost per loo pounds . . 

Period cost per loo pounds. . . 

Weekly pounds melted to 
pounds fuel 

Period pounds melted to 
pounds fuel 



Oct. 9 



Pounds 



149,280 



Amount 



45-65 
1.80 

5.73 

53.50 

1.82 



3.20 
1.64 
2.63 

30.00 
2.00 
2.90 

10-95 

8.66 

.53 



10.20 
6.15 



12.42 
199.78 



8.7 



Oct. 16 



Pounds 



150,441 
299,721 



Amount 



18.51 
55.97 



.90 
2.00 
2.63 

30.00 



10.75 

8.52 

.80 



10.20 
6.15 

12.42 
203.55 
403.33 



• 135 
.135 



8.4 
8.5 



Oct. 23 



Pounds 



116,451 
416,172 



Amount 



9 


.22 


44 


08 


8 


25 


I 


53 


2 


63 



9.30 
6.93 

.44 



10.20 

6.15 

12.42 
174.85 
578.18 



• IS 

.139 



8.3 

8.5 



Moulding Expense 



619 



Moulding — Section B. Form i 





Oct. 9 


Oct. 16 


Oct. 23 




Pounds 


Amount 


Pounds 


Amount 


Pounds 


Amount 


Bench Moulding 




884.80 

10.00 

6.58 
2.42 
7.50 
2.60 

23.16 

46.37 

6.30 

.47 

2.30 

30.58 

41.94 
192.22 

21.8 




858.80 
1743.60 

10.00 

6.88 
2.80 

10.48 
23.54 

50.83 
6.88 

.40 

1.65 
30.58 

41.94 
185.98 
387.20 

21.7 
21. 1 




715.40 
2459.00 

5.00 

1. 15 

1.09 

1.60 

8.19 

37-77 

6 10 


Period productive labor 

Moulding Expense on 
Productive Labor 

Non-pruductive labor 

Flasks, snap boards and 

matches 

Miscellaneous supplies 

Ladles 

Shovels and screens 

Rammers. 

Charges from other depts — 
Making bottom boards for 
. moulding machines 


Sand 

Handling sand 


Handling weights and bands. 

Reclaiming sand 

Parting sand. 

Interest on investment 

Heat, light and power. 
Taxes, insurance and depre- 
ciation 


.62 

30.58 

41.94 
134 04 


Weekly expense 






Per cent moulding expense to 


18.7 


Period per cent moulding 
expense to prod, labor 


20.8 



620 



Foundry Accounts 



Cleaning and Tumbling — Section C. Form i 



Productive labor 

Number of pounds cleaned 
and tumbled 

Period pounds cleaned and 
tumbled 

Cost per 100 pounds (if day- 
work) 

Period cost per lOO pounds 
(if day work) 

Cleaning and Tumbling 
Expense 

Supplies. 

Overseeing 

Non-productive labor 

Charges from other depts. . . 

Tumblers 

Stars for tumbling 

Interest on investment 

Heat, light and power 

Taxes, insurance and depre- 
ciation 

Weekly gross expense 

Stars used in No. 3. 

Weekly expense 

Period expense 

Weekly expense cost per loc lbs 

Period expense cost per 100 
pounds 

Weekly total cleaning and 
tumbling cost 

Period total cleaning and 
tumbling cost 



Oct. 9 



Pounds 



134,462 



Amount 



74.62 



.056 



S.44 
55.44 



8.40 
71.73 



71.73 
.053 



.109 



Oct. 16 



Pounds 



139,089 
273,551 



Amount 



70.92 



.053 
.054 



.40 

.40 

.65 

4.00 

S.44 
55.44 

8.40 
74.73 

74.73 
146.46 
.053 

.053 

.106 

.107 



Oct. 23 



Pounds 



105,203 
378,754 



Amount 



.054 
• 053 



1.93 

.75 

2.02 

10.00 

S.44 

55.44 

8.40 
73.98 

73.98 

220.44 

.07 

.058 

.124 

III 



Pickling Expense 



621 



Pickling — Section C — No. 2. Form i 



Weekly prod, labor 

Period prod, labor 

Weekly pounds pickled 

Period pounds pickled 

Weekly cost per loo. pounds 

(if day work) 

Period cost per loo pounds 

(if day work) 

Pickling Expense 

Non-productive labor 

Oil of vitriol 

Hydrofluoric acid. 

Acid spigots. 

Charges from other depts. . . , 

Interest on investment 

Heat, light and power 

Taxes, insurance and depre- 
ciation 

Total weekly expense 

Total period expense 

Per cent dept. expense to 
prod, labor 

Period per cent dept. expense 
to prod, labor 



Oct. 9 



Pounds 



62,818 



Amount 



20.70 



1-75 
2.06 
23.92 



3.40 
3.08 



2.53 
36.74 



177. 5 



Oct. 16 



Pounds 



65,600 
128,418 



Amount 



19.82 
40.52 



.030 
.032 



15.28 

1.88 
3.40 
3.08 

2.53 
26.92 
63.66 

I3S.8 . 

ISS.8 



Oct. 23 



Pounds 



36,220 
164,638 



Amount 



13.10 
53.62 



.036 
.034 

1. 10 

lo.si 

1.48 
3.40 
3.08 

2.53 
22.10 
85.76 



168.7 
160 



622 Foundry Accounts 

Sand Blasting — Section C — No. 3. Form i 



Weekly prod, labor 

Period prod, labor 

Weekly pounds sand blasted 
Period pounds sand blasted . 
Weekly cost per loo pounds 

(if day work) 

Period cost per loo pounds 

(if day work) 

Sand Blasting Expense 

Non-productive labor 

Supplies 

Sand 

Charges from other depts . . . 

Interest on investment 

Heat, light and power 

Taxes, insurance and depre- 
ciation 

Total weekly expense 

Total period expense 

Per cent dept. expense to 
prod, labor 

Period per cent dept. expense 
to prod, labor 

Prod. labor 



Oct. 9 



Pounds Amount 



.043 



• 75 
1. 10 



6.80 
IS. 40 



1.38 
25.43 



581.9 



Oct. 16 



Pounds Amount 



11,800 
22,000 



6.06 
10.43 



.051 
.048 



.61 



6.80 
15.40 

1.38 
25.29 

SO. 72 

417.4 

486.3 
486.3 



Oct, 23 



Pounds Amount 



8,100 
30,100 



4.61 
15.04 



.057 
.05 

.41 

1. 10 

6.80 
15.40 

1.38 
25.09 
75.81 

544.2 

S04.2 
504.2 



Core-Making Expense 
Core Department — Section D. Form i 



623 





Oct. 9 


Oct. 16 


Oct. 23 




Pounds 


Amount 


Pounds 


Amount 


Pounds 


Amount 


Productive labor 




233.55 

24.00 
12.65 
19.14 
12.10 
17. II 
21.80 
2.92 
6.44 

5.54 

13.67 
1.43 

21.61 
158.41 

67.8 




220.65 
454.20 

24.00 
12.63 
18.08 
11.78 
15.16 
18.32 
2.45 
5.58 

3.00 

13.67 
1.43 

21.61 

147.71 
306.12 

66.9 

67.4 
67.4 




16S.6S 
619.85 

24.00 
7.87 

13.89 
9.62 

13.37 

25.89 
1.56 
1.73 

1. 55 

13.67 
1.43 


Period productive labor 

Core Making Expense 


Tending ovens 

Inspecting cores 

Storing cores 


General labor 


Sand 


Coke ... . 


Coal 


Rosin. 

Miscellaneous supplies 

Flour. 

Interest on investment 

Heat, light and power 

Taxes, insurance and depre- 


Weekly core making expense. 

Period core making expense. . 

Weekly per cent expense to 

prod, labor 


136.19 

442.31 

82 '' 


Period per cent expense to 
prod. labor .... 


71.3 
71.3 







624 



Foundry Accounts 



General Expense — Section E. Form i 



Executive 

Foreman 

9396— 2— B. 

Non-productive labor 

Clerical 

Supplies 

Charged from other Depts. 

Scrap 

Gas 

Inspecting 

Injured employee 

Tending pattern safe 

Brooms 

Interest on investment 

Heat, light and power 

Taxes, insurance and depre- 
ciation 

Weekly general expense 

Period general expense 

Weekly prod, labor 

Period prod, labor. 

Per cent expense to prod, 
labor 

Period per cent expense to 
prod, labor 



Oct. 9 



Pounds Amount 



27.00 
48.00 

12.74 
49.00 
.87 
IS. 55 
45.38 
1. 00 
63.20 

11.47 

11.56 

22.59 

310.45 
618.81 

984.49 



62.9 



Oct. 16 



Pounds Amount 



27.00 
48.00 

25.08 

49- 00 
1.43 

26.00 
3.57 
1. 00 

64.59 

9.60 
11.56 

22.59 

310.45 
599.87 
1218.68 
955.60 
1940.09 

62.8 



Oct. 23 



Pounds Amount 



27.00 
48.00 

16.67 
49.00 

1. 8s 
27.75 
13.98 

1. 00 
42.6s 

5. 00 

7.20 

• 75 

11.56 

22.59 

310.45 
585.45 

1804.13 
790.25 

2730.34 

73.9 
65.8 



Individual Job of Casting Cost. Form 2 

Date, Oct. 12 
150 Blocks — J. & 8. Co. — 850 pounds 



Amount 



Unit cost 



Value 



Metal 

Melting expense 

Moulding 

Motilding expense 

Cores 

Cores, expense 

Cleaning and tumbling. 



850 



Cleaning and tumbling expense. 

Sand blasting. 

Sand blasting expense. 

Pickling 

Pickling expense 

General expense 

Spoiled work 

Total 

Cost per pound 



.83 per 100 
. 139 per 100 

20.8% 

71.3% 

.053 per 100 

pounds 

. 058 per 100 

pounds 



.034 

160% 
65.8% 



7-05 

1. 18 

3.00 

.62 

• SO 
.36 

• 45 
.49 



.29 



2.13 

.42 3 spoiled 
16.95 
• 0199 



Note. — In this case no selling expense is added, as it might be in many cases. 



A Successful Foundry Cost System 625 

Monthly Showing. Form 3 
Quick Assets. 
Cash. 
Accounts Receivable. 

Permanent Assets. 
Real Estate. 
Building. 
Machinery. 

Raw Material on Hand. 

Pig Iron, (Credit amount used each week as per costs and charge 

to Mfg. Acct.) 
Scrap. 

Manufacturing Acct. (See analysis below.) 

Expenses undivided (meaning expense supplies not used). 
Quick Liabilities. 

Accoimts Payable. 
Permanent Liabilities. 

Capital. 

Depreciation. 

Surplus. 

Details of Mfg. Acct. 

Dr. 
Inventory at start of castings in process. 

Metal 1 

Labor ? each month. 

Expense ) 

Cr. 

Sales. 

Inventory of castings in process ist of each 
month. 

Balance Profit or Loss monthly. 

A SUCCESSFUL FOUNDRY COST SYSTEM 

By J. P. Golden, Columbus, Ga. 
"... The system consists of, first: a Daily Cupola Report, the 
printed form having column for charge, number of poimds coke and 
brand, pounds pig iron and brand, and per cent silicon and sulphur, 
scrap, foreign and returns, and total charge also hues for weekly totals 
for use in weekly report. Ratio of coke to iron. Time blast started. 
Time bottom dropped. Average blast pressure. Per cent sulphur in 
heat. Per cent silicon in heat. Remarks. With each sheet signed by 
foreman. 



626 Foundry Accounts 

"Second: The Daily Foundry Report, which is made up by the 
Riunbhng Room foreman. This report consists of a sheet, with columns 
for name of moulder, hoiur or piece rate, niunber of moulds, number of 
castings, time of helper, pattern description with columns for weights 
of the various classes of work, as pulleys, sheaves, hangers, hanger 
boxes, pillow blocks, couplings, cane mills, factories, miscellaneous, 
etc. Also colmnn for number of pieces lost, total weight of each kind 
of piece lost, and a cause column for same, showing if it did not run, if 
it was crushed, blowed, or whatever cause of defect. There is a line 
at bottom of sheet for weekly totals to be used in weekly report. The 
daily foundry report furnishes a ready means of comparison of each 
moulder's record, with his own, or with other moulders as to quantity of 
good castings, castings lost, weight and cost of same. This report also 
shows the amount of good and bad castings for each day, in each class, 
with the weekly total for each. 

'^ Third: There is a book for defective and other castings returned 
from shop and customers, in which is the following rule: 

'AH castings returned by machine shop and customers, before 
being made over, must be entered in this book, giving cause for 
making over. Castings returned to foundry from shop or cus- 
tomers, through no fault of foundry, must not be deducted from 
net foundry castings, and should be considered as foreign scrap. 
If fault of foundry, they are charged back to foundry and are con- 
sidered as foundry return scrap.' 

This book has columns for showing date returned, by whom, descrip- 
tion, cause and weight. Without this book, there could be returned 
defective castings, which were the foundry's fault and made over with- 
out the superintendent's knowledge. With the "to be made over" 
casting book, all castings returned are specified therein. If the fault 
of the machine shop, it is so stated. If returned from customers, this 
is noted with date, description, cause and weight. No casting is made 
over without being recorded in this book. This book, being always open 
to superintendent and foreman, saves inquiries and explanations. . . . 

^^ Fourth: The Weekly Foundry Report Sheet. This sheet is made 
up from the daily foundry report, and cupola sheets and the book (to 
be made over castings). On this sheet, provision is made for record 
of bad castings returned from foundry, shop or customer, by classes, 
as well as the good castings made. The total of good castings minus 
defective castings gives net good castings for week. The average per 
cent of all castings lost is given, with the per cent loss in each class, with 
the total pounds pig and foreign scrap charged in cupola, and the net 



A Successful Foundry Cost System 627 

good castings deducted therefrom, we find the per cent lost in remelt, 
cupola droppings, gangways, etc. The weekly foundry report also has 
a record of total melt taken from daily cupola sheet, which with net 
good castings deducted gives per cent, bad castings, gates, etc., of total 
melt, including foreign scrap, returns and pig. In a division headed 
cupola charge is given the number of pounds pig iron, foreign scrap and 
coke, with current price of each and total cost per week. To these 
amounts are added the total wages, giving a total of material and wages 
for week, which divided by the net good castings gives the cost per 
100 pounds, net castings, including pig iron, scrap, coke, wages. 

"The weekly report also has separate divisions for non-producers, 
rumbling department, moulding department, core shop, day and night 
cleaning gangs, in which the wages of each class of men in each division 
are given separately, by total, and the wage cost per hundred pounds. 
. . . The weekly report also embodies the grand total wages cost per 
100 pounds, and this is the most important item, for both foreman and 
superintendent, for this item is one which the foreman can control to 
the greatest extent, and which speaks the loudest in favor of the system. " 

"... In connection with the weekly report is a detailed report of 
the pounds of good castings, to whom sold or charged, and price for each 
lot, and from this sheet is prepared, on the back of the weekly report, 
a statement giving the estimated profit or loss for week." 

"And lastly, there is a ready reference sheet (headed Comparison of 
Per cents, Wages Cost per 100 Pounds in Different Departments of 
Foundry from Weekly Foundry Report) giving the comparison by 
weeks and the average comparison at the end of each year of the fol- 
lowing items after date. Net good castings for week, castings killed, 
in machine shop with columns for the per cent loss of each of the several 
classes of castings, each class in a separate column, gives a ready means 
of comparison in that class for all of its weeks. 

"There are also columns for the cost per week per 100 pounds, net 
castings including pig iron, scrap, coke and wages, the wage cost per 
100 pounds, in the non-producers, rumbling and moulding departments, 
also the core shop, day and night cleaning gangs with a column for 
grand total wage cost per 100 pounds. 

"Both the superintendent and foreman have access to the several 
reports giving each the means of knowing the actual conditions in all 
departments of the foundry at all times. ' 

"This system gives the foreman the means of remedying a small or 
defective output by the knowledge of the cause producing it, and to 
place each moulder upon the class of work to which he is best fitted to 
increase the general output." 



628 



Foundry Accounts 



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Castings To Be Made Over 



629 



"... The system furnishes a basis for closer estimates than formerly 
upon work a little out of the usual run, by knowing exactly what prices 
can be accepted for the regular work. The foundry foreman in this 
case is allowed nominal control of the foundry, hiring and discharging 
his men, fixing their wages, and increases in pay for his men are by his 
recommendations subject to approval of superintendent. ..." 



SAMPLE SHEET FROM ''CASTINGS RETURNED FROM 
SHOP AND CUSTOMERS, TO BE MADE OVER." 

Note: All castings returned by machine shop and customers, before 
being made over, must be entered in this book, stating cause for being 
made over. 

Castings returned to foundry from shop or customers, through no 
fault of foundry, must not be deducted from net foundry castings, but 
should be considered as foreign scrap; but if fault of foundry, they 
should be charged back to foundry, and considered as foundry return 
scrap. 

All castings returned by shop or customers, in excess of number 
ordered, will be charged to foundry the same as defective castings, and 
placed in foundry return scrap, unless otherwise ordered by superin- 
tendent. 

Sample of Entry 



Date 
returned 


By whom 
returned 


Description 


Cause 


Whose fault 


Weight, 
pounds 


April 26, 1909 


Our Mach. shop 


I S. B. pulley 
36x8-2^6 
in. bore 


Bored too 
large 


Mach. shop 


240 


April 29, 1909 


Our Mach. shop 


I split pulley 
24X6-2fi6 
in. bore 


Broke lug 
in split- 
ting 


Mach. shop 


120 


May 3, 1909 


Customer 


12 gear castings 
P. 2 


Cored too 
large 


Foundry 


14 


May 5, 1909 


Foundry 


I D. B. pulley 
36X8-215^6 
in. bore 


Blow hole 
in face 


Foundry 


260 



630 Foundry Accounts 

WEEKLY FOUNDRY 

GoLDENs' Foundry and Machine Co., Columbus, Ga. 

For Week Ending Friday, 19 



Bad castings returned from foundry. 

Total pounds good castings made. 

Defective castings returned from shop and customers 

Net good castings for week. Total amount ( ) 



Total pounds pig and foreign scrap charged in cupola. 
Net good castings for week. 



Per cent lost in re melt, cupola droppings, gangways, etc. 



Per cent bad castings, gates, etc., of total melt. 
Including foreign scrap, rettirns and pig. 



Average per cent of cast- 
ings lost. 



Remainder. 



Total melt. 

Net good castings. 







Proportionate Wage Cost Per Hundred 


No. 


Non-producers 


Wages 






Foundry foreman. 
Foundry assistant. 
Pulley man. 
Crane man. 




$ 


- 




Clerk. 

Cupola tender. 
Cupola helpers. 
Carpenters. 
Watchman. 




Total $ 


Wages cost perj 
• hundred pounds > $ 
net castings. ) 


No. 


Rumbling Departmeni 


Wages 






Foreman. 
Assistant. 
Men. 




1 ] 

J 
Total $ 


Wages cost per 
hundred pounds 
net castings, 
chipped, cleaned, 
and ready to ship. 

Grand Total Wo 


ge Cost 



Note. — Castings returned to foundry from our shop and customers, through no 
fault of foundry, must not be deducted from net foundry castings, and should be 



Weekly Foundry Report 



631 



REPORT 





1 
& 


1 


1- 


SI 


ii 




3 

a 
a 


Ph 


'31 
■g,S 






























Cupola Charge 


Pounds pig iron @ per hundred $ -j Cost per hundred ■ 
Pounds foreign scrap @ per hundred 1 pounds net castings 
Pounds coke @ per hundred j including pig iron, j 
Total wages $ J scrap, coke, wages. J 
Total $ 
Material cost per hundred pounds net castings made as per sheet. $ 
Total cost per hundred pounds net castings made as per sheet. $ 


$ 



Pounds in Different Departments 



No. 



Moulding Department 



Wages 



Moulders (white). 
Helpers (white). 
Helpers (black). 



Total $ 



Wages cost per ] 
hundred pounds | $ 
net castings. 



No. 



Core Shop 



Wages 



Foreman. 
Core makers. 
Help. 



Total $ 



Wages cost per ^ 
hundred pounds > $ 
net castings. ) 



No. 



Night Cleaning Gang 



Wages 



Headman. 
Men. 



Total $ 



^ Wages cost per l 
> hundred pounds [ $ 
) net castings. ) 



No. 



Day Cleaning Gang 



Wages 



Headman. 
Men. 

per Hundred Pounds $ 



$ 
Total $ 



Wages cost per ' 
hundred pounds [ S 
net castings. 



put in foreign scrap pile. Weekly foundry report, made up from daily foundry re- 
port and cupola sheet. 
Pounds castings " killed " in machine shop. 



Ik 



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H PM 



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19 . 

Goldens' 

Foundry & 

Machine Co. 

Week 

ending 





CHAPTER XXVIII 
PIG IRON DIRECTORY 

The Classification and Directory of Pig Iron Brands given herewith 
are taken from Professor Porter's Report. 

"Pig Iron is classified as: 
First. — Cold, Warm or Hot Blast. 
Second. — Coke, Anthracite or Charcoal. 
Third. — Sand or Machine. 
Fourth. — Basic, Bessemer, Malleable, Foundry or Forge. 

"It is only necessary to define the fourth classification as the others 
are self-explanatory. " 

"Basic iron means primarily one with low silicon. The standard for 
this grade having silicon under i per cent and sulphur under 0.05 per 
cent." 

" Bessemer iron means primarily phosphorus under i per cent. Stand- 
ard Bessemer contains from i to 1.25 per cent silicon with sulphur 
under 0.05, but the grade is essentially based on low phosphorus. Irons 
with extra low phosphorus and variable siHcon are sometimes designated 
as low phosphorus irons." 

"Foundry and Forge Irons embrace practically everything in the way 
of ordinary iron, these grades being subdivided on the basis of siHcon 
and sulphur content." 

"The following subclassification of Foundry and Forge iron has been 
agreed upon by the blast furnace interests of the districts indicated: 

Classification and Grades of Foundry Iron 



Southern Points 

No. I foundry 

No. 2 foundry 

No. 3 foundry 

No. 4 foundry 

Gray forge 

No. I soft 

No. 2 soft 



Silicon, per cent 


Sulphur, per cent 


2.75-3.25 


.05 and under 


2.25-2.75 


.05 " 


1.75-2.25 


.06 " 


1.25-2.00 


.07 " 


I. 25-1. 75 


.08 " 


3 . 00 and over 


.05 " 


2.5(^3.25 


.05 " 



633 




634 Pig Iron Directory 

Classification and Grades of Foundry Iron (Continued) 



Eastern Points 

No.iX 

No. 2X 

No. 2 plain 

No. 3 foundry 

No. 2 mill 

Gray forge 

Mottled and White by Fracture, Cen- 
tral West and Lake Points 

No. I foundry 

No. 2 foundry 

No. 3 foundry 

Gray forge 

Buffalo Grading 

Scotch 

No. I foundry 

No. 2 foundry 

No. 2 plain 

No. 3 foundry 

Gray forge 



Silicon, per cent 



2.75 and up 

2.25-2.75 

1.75-2.25 

I .25-1. 75 

1 . 25 and under 

1.50 " 



2.25-2.75 
1.75-2.25 
1 . 75 and under 



3 . GO and over 
2.50-3.00 
2.00-2.50 
1.50-2.00 
1.50 (under) 



Sulphur, per cent 



030 and under 
045 " 
050 " 
065 " 
065 " 
065 and up 



. 05 and under 

.05 " 

.05 " 

. 05 and over 



. 05 and under 

.05 " 

.05 " 

.05 " 

.05 " 

. 05 and (over) 



Note. — If sulphur is in excess of maximum, it is graded as lower 
grade, regardless of silicon. 

"Charcoal is not as a rule graded according to the above table but is 
sold by fracture, by analysis, by chill tests, or by some special system 
of grading according to the custom of the maker and demand of the 
purchaser. " 

" It will be noted that so far as Foundry iron is concerned the grading 
system is based exclusively on silicon and sulphur. One reason for 
this is that the phosphorus and manganese are fixed by the composition 
of the ores used, whereas the silicon and sulphur can be varied at will 
by shght changes in the method of operating the furnace. Since in 
many, perhaps, the majority of, cases a blast furnace will be limited 
to a very few ores as a source of supply, it follows that it will be limited 
also in the range of phosphorus and manganese in the iron it produces. 
For this reason, a given brand of iron will usually run fairly constant 
as regards phosphorus and manganese, although its silicon and sulphur 
can be varied at the wish of the management. However, this condition, 
while common, is not imiversal, for some concerns possess a variety of 
ores and can by mixing them produce iron of any composition desired. 



Coke and Anthracite Irons 635 

"In using this directory please bear in mind that it is not infallible. 
Much of the data has been difficult to get, a few concerns refusing abso- 
lutely to furnish information. Again, in some cases time brings changes 
in ownership and character of ore supply, etc., and of course, these 
things will affect the character of the product. In spite of these defic- 
iencies, however, it is believed that the following tables represent the 
most accurate information along these lines available at the present 
time and that they will be found of considerable value." 

"Finally, it must be emphasized that the use of the data is not to tell 
the foundryman the exact analysis of any carload of any brand, but 
rather to help him locate those brands which have, or can be made to 
have a composition suitable for his work." 

"In these tables the percentage of sulphur is not usually given. It 
should be understood that all furnaces strive for, and usually obtain, 
low sulphur in their iron. Practically all foundry grades are sold on the 
understanding that the sulphur is under 0.05 per cent and hence no 
useful purpose is served in giving the sulphur range except in a very 
few cases where it normally runs unusually low." 



Coke and Anthracite Irons 

Adrian. — Adrian fee., D.uBois, Pa. (A-drian fee. Co.) 

Hot blast coke, sand cast, foundry iron, from Lake Superior ores. 
Sil. 1.0-4.0% Mang. 0.4-1.2% Phos. 0.4-0.9% 

Alice. — Alice fee., Birmingham, Ala. (Tenn. Coal, Iron & Ry. Co.) 
Hot blast, coke, sand or chill cast iron, from Ala. red and brown ores. 
Fdry. Sil. 1.0-4.0% Mang. 0.1-0.4% * Phos. 0.71-0% 

Basic Under 1% 0.1-0.4 Under 1% 

Alice. — AHce fee., Sharpsville, Pa. (The Youngstown Sheet & Tube 
Co.) 

Hot blast, coke iron, from Lake Superior ores. 

Usually make Bessemer only for use in their own steel works. 

Alleghany. — Alleghany fee., Iron Gate, Va. (Oriskany Ore & Iron Co.) 
Hot blast, coke, sand cast, foundry iron, from local brown ores. 
Sil. 1.0-4.0% Mang. 0.7-1.5% Phos. 0.2-0.6% 

Allegheny. — McKeefrey fee., Leetonia, O. (McKeefrey & Co.) 

Hot blast, coke, sand cast, foundry iron, from Lake Superior ores. 
Sil. 0.7-2.0% Mang. 0.4-0.8% Phos. 0.4-0.7% 

* Sometimes higher. 



636 Pig Iron Directory 

Andover. — Andover fee., Phillipsburg, N. J. (Andover Iron Co.) 

Hot blast, coke, sand cast, foundry iron, from local magnetic ore, 

Lake Superior ore, iron nodules and roll scale. 
Sil. 1.5-4.0% Mang. 0.6-1.5% Phos. 0.6-0.9% 

A. R. Mills. — (2 stacks), Allentown, Pa. (Allentown Rolling Mills Co.) 
Hot blast, anthracite and coke iron, from local hematites and N. J. 
and N. Y. magnetites. 
Ashland. — Ashland fees. (2 stacks), Ashland, Ky. (,Ashland Iron & 
Min. Co.) 
Hot blast, raw coal and coke, sand cast iron, from local brown and 

Lake Superior ores. 
High Sil. Fdry. Sil. 5.0-12.0% Mang. 0.5-0.8% Phos. 0.5-0.9% 
Bess. Ferro Sil. 9.0-14.0% 0.5-0.8% under 1.0% 

Aurora. — Aurora fee., Columbia, Pa. (Susquehanna Iron Co.) 

Hot blast, anthracite and coke, forge and foundry iron, from native 

and Lake Superior ores. 
Not in operation, March, 1910. 
Battelle. — Battelle fee., Battelle, Ala. (Lookout Mt. Iron Co.) 

Hot blast, coke, sand cast, foundry iron, from local red hematite. 
Not in operation March, 1910. 
Bay View. — Bay view fees. (2 stacks), Milwaukee, Wise. (lUinois 
Steel Co.) 
Hot blast, coke, sand cast iron, from Lake Superior ores. 
Mall. Bes. Sil. 1.0-3.0% Phos. under 0.20% Mang. 0.50-1.0% 
Fdry. 1.0-3.0% over 0.50% 0.50-1.0 

Belfont. — Belfont fee., Ironton, O. (Belfont Iron Works Co.) 

Hot blast, coke, fdry iron, sand cast, from Lake Superior and native 

ores. 
Sil. 1.50-2.50% Phos. 0.40-0.70% Mang. 0.50-0.90% 

Bellefonte. — Bellefonte fee., Bellefonte, Pa. (Bellefonte Furnace Co.) 
Hot blast, coke, sand cast, foundry iron, from native and Lake 

Superior ores. 
Sil. 1.75-4-0% Phos. 0.5-0.7% Mang. 0.5-0.7% 

Belmont. — Belmont fee., Wheeling, W. Va. (Wheeling Iron & Steel 
Co.) 
Hot blast, coke, sand cast, from Lake Superior ores. 
Make only iron for their own steel plant. 

Bessemer.— Bessemer fees. (5 stacks), Bessemer, Ala. (Term. C. I. 
& Ry. Co.) 
Same as De Bardeleben, which see. 



Coke and Anthracite Irons 637 

Bessie. — Bessie fee., New Straitsville, O. (Bessie Ferro Silicon Co.) 
Hot blast, coke and raw coal, sand cast, ferro silicon, from Lake 

Superior low phos. ore. 
Sil. 8.0-14.0% Phos. under 0.10% Mang. under 1.0% 

Big Stone Gap. — Union fee. No. i, Big Stone Gap, Va. (Union Iron 
and Steel Co.) 
Hot blast, coke, sand cast, fdry iron, from local fossil brown ores. 
Sil. usually high Phos. 0.40-0.80% Mang. 0.40-1.0% 

Bird. — Bird fee., Culbertson, O. (The Bird Iron Co.) 

Hot blast, coke, sand cast, fdry iron, from Lake Superior and native 

ores. 
Not in operation March, 19 10. 

Boyd. — Ashland fees. (2 stacks), Ashland, Ky. (Ashland I. & Miu. 
Co., Inc.) 
Hot blast, raw coal and coke, sand cast, fdry iron, from Bath Co. 
I & Lake Superior ores. 
Sil. 1.50-3.0% Phos. 0.40-0.90% Mang. 0.50-0.80% 

Brier Hill. — Grace fee., No. 2, Youngstown, O. (The Brier Hill I. & 
C. Co.) 
Hot blast, coke basic and Bessemer iron, from Lake Superior ores. 

Bristol. — Bristol fee., Bristol, Tenn. (Va. Iron, Coal & Coke Co.) 
• Hot blast, coke, from local brown ores. 
Fdry. Sil. 2.0-2.75% Phos. abt. 0.50% 

Basic (chill cast) low abt. 0.60% 

• Mang. abt. 0.75% 
1.0-1.50% 

Brooke. — Brooke fees. (2 stacks), Birdsboro, Pa. (E. & G. Brooke Co.) 
Hot blast, anthracite and coke, from Lake Superior, Newfoundland 
and magnetic ores. 

Buckeye. — Columbus fees. (2 stacks), Columbus, G. (The Columbus 
L&S. Co.). 
Hot blast, coke, chill mold iron, from Lake Superior ores. 
Fdry Sil. 1.0-3.0% Phos. 0.40-0.60% Mang. 0.60-0.80%* 

Mai. Bes. 0.50-2.50 under 0.20 0.60-1.0. f 

Basic under i.o under 0.20 0.80-1.0 

Stand. Bes. 1.0-2.0 under o.io 

* Sometimes iigher. t Higher or lower if desired. 



6sS Pig Iron Directory 

Buena Vista. — Buena Vista fee., Buena Vista, Va. (Oriskany Ore & 
Iron Co.) 

Hot blast, coke, chill, and sand cast iron, from Oriskany brown 

hematite. 

Fdry. Sil. 1.0-4.0% Phos. 0.2-1.0% Mang. 0.6-1.5% 

Basic under i.o 0.2-0.5 0.6-1.5% 

Spec, car wheel i. 0-1.50 0.2-0.5 0.6-1.5 

Buffalo. — BuQalo Union fee. (3 stacks), Buffalo, N. Y. (The Buffalo 
U. F. Co.) 
Hot blast, coke, sand east iron, from Lake Superior ores. 
Fdry. Sil. 1.50-3-25% Phos. 0.40-0.70% Mang. 0.50-1.0% 

Mai. 0.75-2.0 0.10-0.20 0.40—1.0 

Burden. — Burden fee., Troy, N. Y. (The Burden Iron Co.) 

Hot blast, mixed anthracite coal and coke, occasionally coke alone. 
Magnetic concentrates from northern New York. 
Out of operation March, 19 10. 

Carbon. — Carbon fee., Perry ville, Pa. (Carbon Iron & Steel Co.) 

Hot blast, anthracite coal and coke foundry iron, magnetic from 

N. J. & Lake Champlain, Lake Superior, and foreign ores. 
Sil. 1.50-3.00% Phos. 0.40-0.90% Mang. 0.40-0.90% 

Carondelet. — Missouri fee., So. St. Louis, Mo. (St. Louis Blast Fee. 
Co.) 

Hot blast, coke, Missouri red and brown hematite. 

Analysis refused. 
Chateaugay. — Standish fee., Standish, N. Y. (Northern Iron Co.) 

Hot blast, coke, sand east, foundry iron, from local magnetic ores. 

Sil. 1.0-3.0% Phos. 0.02-0.035% Mang. 0.15-0.50% 

Chattanooga. — Chattanooga fee., Chattanooga, Tenn. (The Southern 

I. & S. Co.) 
Hot blast, coke, sand cast, foundry iron, from Alabama red and 

Georgia brown hematite. 
Sil. 1.50-3.50% Phos. 1.0-1.5% Mang. 0.6-1.0%* 

Cherry Valley. — Cherry Valley fee., Leetonia, O. (United I. & S. Co.) 
Hot blast, coke, sand east, foundry iron, from Lake Superior ores. 
Sil. as desired Phos. 0.20-0.60% Mang. 0.60-0.80% 

Chickies. — Chickies fees. (2 stacks), Chickies, Pa. (Standard Iron 
Min. & Furnace Co.) 
Hot blast, anthracite and coke, sand east, foimdry iron, from mag- 
netites. 

* Sometimes higher. 



Coke and Anthracite Irons 639 

Citico. — Citico fee., Chattanooga, Tenn. (Citico Furnace Co.) 

Hot blast, coke, sand cast, soft foundry, from red and brown hema- 
tites from Tennessee and Georgia. 
Sil. 2.0-3.0% Phos. abt. 1.25% Mang. abt. 0.60% 

Claire. — Claire fee., Sharpsville, Pa. (Claire Furnace Co.) 

Hot blast, coke, Bessemer iron only, from Lake Superior ores. 

Cleveland. — Cleveland fees. (2 stacks), Cleveland, O. (Cleveland Fur- 
nace Co.) 
Hot blast, coke, from Lake Superior ores. 
Analysis refused. 

Clifton. — Clifton fees. (2 stacks). Iron ton, Alabama. (Alabama Con- 
sol. C. & I. Co.) 
Hot blast, coke, sand east, foundry iron, from local brown hematite. 
Sil. 1.0-6.0% Phos. 0.35-0.70% Mang. 1.0-2.0% 

Climax. — Hubbard fees. (2 stacks), Hubbard, O. (The Andrews & 

Hitchcock I. Co.) 
Hot blast, coke, sand cast, strong foundry iron, from Lake Superior 

ores. 
Sil. 1.35-1-75% Phos. 0.30-0.40% Mang. 0.50-0.80% 

Clinton. — Clinton fees., Pittsburgh, Pa. (Clinton I. & S. Co.) 

Hot blast, coke, sand east, foundry iron, from Lake Superior 

ores. 
Sil. up to 3.0% Phos. 0.20-0.75% Mang. 0.50-1.0% 

Colonial. — Colonial fees. (2 alt. stacks), Riddlesburg, Fa. (Colonial 
Iron Co.) 
Hot blast, coke, sand cast, foundry iron, from Lake Superior and 

native ores. 
Sil. up to 4.0% Phos. 0.40-0.60% Mang. 0.50-0.80% 

Covington. — Covington fee., Covington, Va. (Low Moor Iron Co. of 
Va.) 
Hot blast, coke, sand cast iron, from native brown hematite. 
Fdry. Sil. 1.5-3.0% Phos. 0.90-1.2% Mang. 0.70-1.0% 

High Sil. silvery 4.0-8.0 0.90-1.2 0.70-1.0 

Cranberry. — Cranberry fee., Johnson City, Tenn. (The Cranberry 

Fee. Co ) 
Hot blast, coke, sand cast, low phos. iron, from local magnetic 

ore. 
Sil. 1.0-3.5% Phos. under 0.035% Mang. 0.4-0.6% 



640 Pig Iron Directory 

'Crane. — Crane fees. (3 stacks), Catasauqua, Pa. (Empire S. & I. Co.) 
Hot blast, anthracite and coke, sand cast iron, from N. J. magnetic, 

Pa. hematite, Lake Superior and foreign ores. 
Fdry. Sil. 0.75-3.50% Phos. 0.60-0.90% Mang. 0,50-2.0% 

Basic mider i.o under i.o 0.50-0.80 

Low phos. 1.0-3.0 under 0.03 0.50-3.0 

Crozer. — Crozer fees. (2 stacks), Roanoke, Va. (Va. Iron, Coal & 

Coke Co.) 
Hot blast, coke, sand cast iron, from Va. limonite, moimtain and 

specular ores. 
Fdry. Sil. 2.10-2.75% Phos. 0.60-0.80% Mang. 0.60-0.90% 

Basic abt 0.70 abt. 0.70 abt. 1.25 

Cumberland. — Cumberland fee., Cumberland Fee. P. O., Tenn. (War- 
ner Iron Co.) 
Hot blast, coke, sand east foundry, from local brown and red hema- 
tites. 
Sil. 2.0-4.5% Phos. abt. 2.0% Mang. abt. 0.30% 

Dayton. — Dayton fees. (2 stacks), Dayton, Tenn. (The Dayton C. & 
I. Co. Ltd.) 
Hot blast, coke, sand east, foundry iron, from Tenn. fossil and 
Georgia hematite. 
De Bardeleben. — Bessemer fees. (5 stacks), Bessemer, Tenn. (Tenn. 
C. I. & Ry. Co.) 
Hot blast, coke, sand and chill east iron, from local red and brown 

hem. 
Fdry. & Mill Sil. up to 3.25% Phos. 0.70-1.0% Mang. 0.10-0.40 
Basic up to 1.0 up to 1.0 0.10-0.40 

Detroit. — Detroit fee., Detroit, Mich. (Detroit Furnace Co.) 

Hot blast, coke, sand cast, foundry iron, from Lake Superior ores. 
Dora. — Dora fee., Pulaski City, Va. (Va. Iron, Coal & Coke Co.) 

Hot blast, coke, sand east foundry iron, from native limonite and 
mountain ores. 

Sil. 1.50-3.00% Phos. 0.40-0.80% Mang. 0.50-0.90% 
Dover. — Dover fee., Canal Dover, O. (The Pa. Iron & Steel Co.) 

Hot blast, coke, sand cast, foundry iron, from Lake Superior ores. 
Dunbar. — Dunbar fees. (2 stacks), Dunbar, Pa. (Dunbar Furnace Co.) 
Hot blast, coke, sand or machine cast iron, from Lake Superior 

specular and soft ores. 
Fdry. Sil. 1.5-3.0% Phos. 0.30-0.60% Mang. 0.30-0.60% 

Malleable 1.0-2.0 under 0.20 0.30-0.80 



Coke and Anthracite Irons 641 

Durham. — Durham fee., Riegelsville, Pa. (Durham Iron Co.) 

Hot blast, anthracite and coke, sand cast iron, from Lake Superior, 
local hematite and New Jersey magnetite. 

Eliza. — Pittsburgh fees. (5 stacks), Pittsburgh, Pa. (Jones & Laughlin 
St. Co.) 
Hot blast, coke, Bessemer and basic, machine east iroij, from Lake 
Superior ores. 

Ella. — Ella fee., West Middlesex, Pa. (Piekands, Mather & Co.) 

Hot blast, coke, foundry and malleable iron, from Lake Superior 

ores. 
On account of the large assortment of ores available, this furnace 

can make practically any desired composition. 

Embreeville. — Embreeville fee., Embreeville, Tenn. (Embree Iron Co.) 
Hot blast, coke, foundry iron, from local brown hematite. 

Empire. — Reading, Pa. (Empire Steel & Iron Co.) 

Hot blast, anthracite and coke, foundry iron, from Lake Superior, 

Porman and magnetic ores. 
Sil. 2.0-3.0% Phos. 1,25-2.50% Mang. 0.50-1.0% 

Emporium. — Emporium fee.. Emporium, Pa. (Emporium Iron Co.) 
Hot blast, coke, foundry iron, from brown hematite. 
Sil. as desired Phos. abt. 0.80% Mang. abt. 0.60% 

Ensley. — ^Ensley fees. (6 stacks), Ensley, Alabama. (Tenn. C. I. & 

Ry. Co.) 

Hofblast, coke, machine cast iron, from red and brown hematite. 
Basic Sil. up to 1.0% Phos. 0.70-1.0% Mang. 0.10-0.40%* 

Fdry. & Mill up to 2.50 0.70-1,0 0.10-0.40* 

Essex. — Northern fee.. Port Henry, N. Y. (Northern Iron Co.) 
Hot blast, coke, foundry iron, from local magnetic ores. 
Sil. 1.0-2.50% Phos. 0.40-0.90% Mang. 0.10-0.40% 

Etowah. — Etowah fees. (2 stacks), Gadsden, Ala. (Ala. Consol.) 

Hot blast, coke, foundry iron, from local red and brown hematite. 
Sil. 1.0-06% Phos. 0.70-1,20% Mang. 0.40-0.80% 

Eureka. — Same as Oxmoor, which see. 

Everett. — Earlston fee., Earleston, Pa. (Jos. E. Thropp.) 

Hot blast, coke, foundry iron, from Lake Superior and local brown 

ores. 
Sil. 1.50-3-50% Phos. 0.40-0.70% Mang. 0,50-0,90% 

* Sometimes higher. 



642 Pig Iron Directory 

Fannie. — Fannie fee., West Middlesex, Pa. (.United Iron & Steel 
Co.) 
Hot blast, coke, foundry iron, from Lake Superior ores. 
Sil. as desired Phos. 0.20-0.60% Mang. 0.60-0.80% 

Federal. — Federal fees. (2 stacks), S. Chicago, 111. (Federal Furnace 
Co.) 
Hot blast, coke, mal. and foundry iron, from Lake Superior ore. 
Sil. as desired. Phos. as desired. Mang. as desired. 

Florence. — Philadelphia fee., Florence, Ala. (Sloss-Sheffield S. & I. 
Co.) 
Hot blast, coke, sand cast, foundry iron, from Ala. brown hematite. 
Sil. as desired.. Phos. 0.80-1.25% Mang. 0.40-0.80% 

Fort Pitt. — Cherry Valley fee., Leetonia, O. (United I. & S. Co.) 
Hot blast, coke, spec, car wheel iron, from Lake Superior ore. 
Sil. as desired. Phos. 0.20-0.80% Mang. 0.60-0.80% 

Franklin. — Franklin fee., Franklin Springs, N. Y. (Franklin Iron 

Mfg. Co.) 
Hot blast, coke, foundry iron, from fossil, red hematite from CHn- 

ton, N. Y. 
Not in operation March, 1910. 
Sil. 2.25-3.0% Phos. 1.25-1.50% Mang. 0.25-0.40% 

Gem. — Same as Shenandoah, which see. 

Genesee. — Genesee fee., Charlotte, N. Y. (Genesee Furnace Co.) 
Hot blast, coke, from Lake Superior ore. 
Not in operation March, 1910. 

Girard. — Mattie fee., Girard, O. (Girard Iron Co.) 

Hot blast, coke, foundry iron, from Lake Superior ore. 

Sil. 1.50-3.0% Phos. 0.40-0.70% Mang. 0.50-0.80% 

Globe. — Globe fee., Jackson, O. (Globe Iron Co.) 

Hot blast, raw coal and coke, sand cast, high silicon silvery iron, 

from native ores. 
Sil. 4.0%-! 2.0% Phos. 0.40-0.80% Mang. 0.40-0.80% 

Grafton. — McKeefrey fee., Leetonia, O. (McKeefrey & Co.) 
Hot blast, coke, foundry iron, from Lake Superior ores. 
Sil. 2.0-2.50% Phos. 0.40-0.70% Mang. 0.40-0.80% 

Graham. — Graham fee., Graham, Va. (Va. Iron, Coal & Coke Co.) 
Hot blast, coke, foundry and basic iron, from Lake Superior and 
native brown hematite. 



Coke and Anthracite Irons 643 

Hamilton. — Hamilton fee., Hanging Rock, O. (The Hanging Rock 
Iron Co.) 
Hot blast, coke, sand cast iron, from native block and limestone 

and Lake Superior ores. 
Fdry. Sil. as desired. Phos. 0.3-0.4% Mang. 0.5-0.7% 

Mall. as desired. under 0.20 

Hector. — Chnton fee., Pittsburgh, Pa. (CKnton Iron & St. Co.) 
Hot blast, coke, foundry iron, from Lake Superior ores. 
Sil. up to 3.50% Phos. 0.50-0.75% Mang. up to 1.0% 

Helen. — Helen fee., Clarksville, Tenn. (Red River Furnace Co.) 

Hot blast, coke, sand cast soft, fluid foundry iron, from local brown 

hematite. 
Sil. 2.0-3.0% Phos. abt. 1.25% Mang. 0.40-0.60% 

Henry Clay. — Henry Clay fees. (2 stacks), Reading, Pa. (Empire 
Steel & Iron Co.) 
Hot blast, anthracite coal and coke, foundry and forge iron, from 

local hematite and magnetite. 
Fdry. Sil. 1.50-4.50% Phos. 2.50-3.50% 

Hillman. — Grand River fees. (2 stacks). Grand Rivers, Ky. (Hillman 
Land & Iron Co.) 
Hot blast, coke, foundry and forge sand east iron, from local brown 

hematite. 
Not in operation March, 19 10. 

Hubbard. — Hubbard fees. (2 stacks), Hubbard, O. (The Andrews & 
Hitchcock Iron Co.) 

Hot blast, coke, malleable iron, from Lake Superior ore. 

Sil. 1.0-2.0% Phos. under 0.20% Mang. under 0.80% 

Hubbard Scotch. — Hubbard fees. (2 stacks), Hubbard, O. (The 
Andrews & Hitchcock Iron Co.) 

Hot blast, coke, soft foundry iron, from Lake Superior ores. 

Sil. up to 3.00% Phos. 0.50-0.65% Mang. about 0.60% 

Hudson. — Secausus fee., Secausus, N. J. (Hudson Iron Co.) 

Hot blast, anthracite coal and coke, foundry iron, from N. Y. mag- 
netite, N. J. limonite and Lake Superior ores. 

Sil. up to 3-4% Phos. 0.60-0.95% Mang. up to 0.50% 

Imperial. — Shelby fee.. No. i, Shelby, Ala. (Shelby Iron Co.) 

Hot blast, coke, iron from local brown hematite. 

Not in operation March, 1910. 
Inland. — Inland fee., Indiana Harbor, Ind. (^Inland Steel Co.) 

Hot blast, coke, basic iron, from Lake Superior ores. 



644 Pig Iron Directory 

Ironaton. — Clifton fees. (2 stacks), Ironaton, Ala. (Alabama Consol. 
C. &. I. Co.) 

Hot blast, coke, foundry iron, sand cast, from local brown ore. 

Sil. 1.0-6.0% Phos. 0.70-0.90% Mang. 0.70-1.0% 

Iroquois. — Iroquois fees. (2 stacks), S. Chicago, 111. (Iroquois Iron 
Co.) 

Hot blast, coke, foundry iron, from Lake Superior ores. 

Sil. 1.35-2-50% Phos. 0.3-0.4%* Mang. 0.40.-0.70% 

Ivanhoe. — Ivanhoe fee., Ivanhoe, Va. (Carter Iron Co.) 

Hot blast, coke, sand cast, foundry iron, from local and Lake 
Superior ores. 

Sil. % as desired. Phos. abt. 0.40% Mang. abt. 0.70% 

Jenifer. — Jenifer fee., Jenifer, Ala. (Jenifer Iron & Coal Co.) 

Hot blast, coke, sand cast, foundry iron from local brown hematite. 

Not in operation March, 1910. 
Jisco. — Jisco fee., Jackson, O. (Jackson Iron & Steel Co.) 

Hot blast, coke and raw coal, high siHcon iron, from native and Lake 
Superior ores. 

Sil. 4.0-14.0% Phos. up to 0.9% Mang. up to 0.9% 

Josephine. — Josephine fee., Josephine, Pa. (Josephine Furnace & 
Coke Co.) 

Hot blast, coke, sand cast iron, from Lake Superior ores. 

Fdry. Sil. up to 4.0% Phos. 0.50-0.80% Mang. under 0.90% 

Bessemer 1.25-2.0 0.085-0.10 under 0.90 

Juniata. — Marshall fee., Newport, Pa. (Juniata Fee. & Fdry, Co.) 

Hot blast, anthracite coal and coke, sand cast, foundry iron, from 
local hematite and Lake Superior ores. 

Sil. up to 2.0% Phos. under 1.0% Mang. under 1.0% 

Lackawanna. — (12 stacks). (Lackawanna Steel Co.) 

Lackawanna fees. (7 stacks), Lackawanna, N. Y. 

Bird Coleman fees. (2 stacks), Cornwall, Pa. 

Colebrook fees. (2 stacks), Lebanon, Pa. 

N. Cornwall fee., Cornwall, Pa. 

Hot blast, coke, Bes. and basic iron, from Lake Superior and Corn- 
wall ores. 

Lady Ensley. — Lady Ensley fee., Sheffield, Ala. (Sloss-Sheffield S. & 
I. Co.) 
Hot blast, coke, sand cast, foundry iron, from local brown hematite. 
Sil. as desired. Phos. 1.0-1.50% Mang. 0.50-0.80% 

* Sometimes higher. 



Coke axid Anthracite Irons 645 

La Follette. — Lsi Follette fee., La Follette, Tenn. (La FoUette C, I. 

& Ry. Co.) 
Hot blast, coke, sand cast, foundry iron, from local fossil, red and 

brown hematite. 
Sil. up to 4.0% Phos. 1.0-1.25% Mang. 0.50-0.75% 

L. C. R. — Lebanon, O. (Lebanon Reduction Co.) 
Coke and charcoal, low phos. pig. 
Operated for experimental purposes only. 

Lebanon Valley. — Lebanon fee., Lebanon, Pa. (Lebanon Valley Fee. 
Co.) 

Hot blast, anthracite coal and coke, sand cast, foundry iron, prin- 
cipally Cornwall ore. 

Sil. as desired. Phos. 0.3-0.4% Mang. p.3-0.4% 

Lees port. — Leesport fee., Leesport, Pa. (Leesport Furnace Co.) 

Hot blast, anthracite coal and coke, sand cast, foundry iron, from 

local hematite and magnetite. 
Sil. as desired. Phos. 0.2-0,3% Mang. abt. 1.00% 

Lehigh. — Lehigh fee., Allentown, Pa. (Lehigh Iron & Steel Co.) 

Hot blast, anthracite and coke, siand cast, foundry and mill iron, 

from Lake Superior, local hematite and New Jersey magnetite. 
Not in operation March, 1910. 

Lone Star. — Sam Lanham fee.. Rusk, Texas. (State of Texas.) 
Hot blast, coke, from local brown hematite. 
Not in operation March, 1910. 

Longdale. — Longdale fee., Longdale, Va. (The Longdale Iron Co.) 
Hot blast, coke, chill cast iron, from local brown hematite. 
"Basic" Sil. under 1.0% Phos. [0.90-1.0% Mang. 1.0-1.5% 
"Off Basic Sil." 1.0-1.75 0.90-1.0 1.0-1.50 

"Off Basic Sul." * 0.25-0.75 0.90-1.0 1.0-1.50 

Lowmoor. — Lowmoor fees. (2 alt. stacks), Lowmoor, Va. (Lowmoor 
I. Co. of Va.) 
Hot blast, coke, sand east iron, from local brown hematite. 
Fdry. Sil. 1.50-3.0% Phos. 0.80-1.0% Mang. 0.90-1.2% 

High Sil. silvery 4.0-8.0 0.80-1.0 0.90-1.2 

Macungie. — Macungie fee., Macungie, Pa. (Empire Steel & Iron Co.) 
Hot blast, anthracite and coke, sand cast, foundry iron, from local 

hematites, Lake Superior and foreign ores. 
Sil. 0.75-3.50% Phos. 0.60-0.90% Mang. 0.50-2.0% 

* Sulphur over .05 per cent. 



646 Pig Iron Directory 

Malleable. — Iroquois fees. (2 stacks), S. Chicago, III. (Iroquois Iron Co.) 
Hot blast, coke, sand cast, foundry iron, from Lake Superior ores. 
Sil. 1.25-2.50% Phos. under 0.2% Mang. 0.40-0.70% 

Mannie. — Aliens Creek fees. (2 stacks), Mannie, Tenn. (Bon Air C. 
& I. Co.) 

Hot blast, coke, sand cast, foundry iron, from local brown hematite. 

Sil. up to 8.0% Phos. abt. 2.0% Mang. 0.40-0.65% 

Marshall. — Marshall fee., Newport, Pa. (Juniata Fee. & Fdry Co.) 

Hot blast, anthracite and coke, sand east, foundry iron, from local 
hematite and Lake Superior ores. 

Sil. up to 3.0% Phos. under 1.0% Mang. under 1.0% 

Martin's Ferry. — Martin's Ferry fee., Martin's Ferry, W. Va. « (Wheel- 
ing Iron & Steel Co.) 

Hot blast, coke, Bessemer only, from Lake Superior ores. 
Ma,x Meadows. — Max Meadows fee.. Max Meadow^s, Va. (Va. Iron, 
Coal & Coke Co.) 

Hot blast, coke, sand cast iron, from Va. limonite and mountain ores. 

Fdry. Sil. 1.75-2.75% Phos. 0.40-0.70% Mang. 1.0-2.0% 

Basic under i.o under i.o Mang. abt. 1.50 

Miami. — Hamilton, O. (Hamilton Iron & Steel Co.) 

Hot blast, coke, iron, from Lake Superior ores. 

Fdry. Sil. 1.0-3.50% Phos. 0.40-0.70% Mang. 0.50-0.80% 

Mall. 0.75-2.0 imdero.2o 0.60-1.0 

Basic imder 1.0 under 0.20 as desired 

Missouri. — Missouri fee., S. St. Louis, Mo. (St. Louis Blast Furnace 
Co.) 

Hot blast, coke, basic iron, from Mo. red and brown hematites. 

Analysis refused. 
Musconetcong. — Musconetcong fee.. Stanhope, N. J. (Musconetcong 
Iron Works.) 

Hot blast, anthracite and coke, foundry iron, from New Jersey 
magnetic. Lake Superior, Cuban and other foreign ores. 

Sil. 2.50-3.50% Phos. 0.60-0.70% Mang. 0.60-0.70% 

Napier. — Napier fee., Napier, Tenn. (Napier Iron Works.) 

Hot blast, coke, foundry iron, from local brown hematite. 

Sil. 2.0-2.75% Phos. 0.75-1.50% Mang. 0.40-0.80% 

Nellie. — Ironton, O. (The Ironton Iron Co.) 

Hot blast, coke, from Lake Superior ores. 

Fdry. Sil. 1.25-3.0% Phos. 0.40-0.60% Mang. 0.50-0.80% 

Mall. Bes. 1.0-2.0 under 0.20 0.50-0.90 



Coke and Anthracite Irons 647 

Nellie. — Alice & Blanche fees. (alt. stacks), Ironton, O. (The Mar- 
ting I. & S. Co.) 
Hot blast, coke, sand cast iron, from Lake Superior and Kentucky 

ores. 
Fdry. Sil. 1.0-3.0% Phos. 0.40-0.60% Mang. 0.50-1.0% 

Mall. 0.50-3.0 under 0.20 0.50-1.0 

Niagara. — Niagara fee., N. Tonawanda, N. Y. (Tonawanda Iron & 
Steel Co.) 
Hot blast, coke, foundry iron, from Lake Superior hematite. 
Analysis refused. 
Nittany. — Same as Bellefonte, which see. 
Norton. — Ashland, Ky. (Norton Iron Works.) 

Hot blast, coke, mall, and Bess, iron, from Lake Superior ores. 
Norway. — Colonial fees. (2 alt. stacks), Riddlesburg, Pa. (Colonial 
Iron Co.) 
Hot blast, coke, foundry iron, from Lake Superior and native ores. 
Sil. up to 4.0% Phos. 0.60-0.90% Mang. 0.70-1.0% 

Oxford. — Oxford fee., Oxford, N. J. (Empire Steel & Iron Co.) 

Hot blast, anthracite and coke, basic iron, from local magnetic and 

special ores. 
Sil. under 1.0% Phos. under 1.0% Mang. 0.75-1.25% 

Oxmoor. — Oxmoor fees. (2 stacks), Oxmoor, Ala. (Tenn. Coal, I. & 
Ry. Co.) 
Hot blast, coke, foundry and forge, sand cast, from red and brown 

hematite. 
Sil. up to 3.50% Phos. 0.70-1.0% Mang. 0.10-0.40%* 

Perry. — Carbon fee., Perryville, Pa. (Carbon Iron & Steel Co.) 

Hot blast, anthracite and coke, Bess, iron, from Lake Superior, 
foreign, Lake Champlain and New Jersey ores. 
Paxton. — Paxton fees. (2 stacks), Harrisburg, Pa. (Central I. & S. 
Co.) 
Hot blast, anthracite and coke, various ores. 

Peerless. — Iroquois fees. (2 stacks), S. Chicago, 111. (Iroquois Iron 
Co.) 
Hot blast, coke, foundry iron, from Lake Superior ores. 
Sil. 3.0-3.5% Phos. 0.30-0.40% Mang. 0.40-0.70% 

Pencost. — Bessie fee., New Straitsville, O. (Bessie Ferro-Silicon Co.) 
Hot blast, coke, ferro-sihcon, from Lake Superior ores. 
Sil. 5.0-12.0% Phos. 0.30-0.70% Mang. under 1.0% 

* Sometimes higher. 



648 Pig Iron Directory 

Pequest. — Pequest fee., Buttzville, N. J. (Pequest Co.) 

Hot blast, anthracite and coke, foundry iron, from N. J. magnetic 

and manganiferous ores. 
Out of blast March, 1910. 

Perry. — Perry fee., Erie, Pa. (Perry Iron Co.) 

Hot blast, coke, sand cast iron, from Lake Superior ores. 
Fdry. Sil. 1.75-3.0% Phos. 0.40-0.70% Mang. 0.40-0.80% 

Fdry. 1.00-2.00 1. 15-0.30 0.40-0.80 

Special '2.00-3.50 1.00-1.50 0.40-0.80 

Pioneer. — Pioneer fees. (3 stacks) , Thomas, Ala. (Republic Iron &S t. Co.) 
Hot blast, coke, foundry iron, from red and brown hematite. 
Sil. up to 3.5o%o* Phos. 0.75-0.95% Mang. 0.40-0.80% 
Poughkeepsie. — Poughkeepsie fees. (2 stacks), Poughkeepsie, N. Y. 
(Poughkeepsie Iron Co.) 
Hot blast, anthracite and coke, from Lake Superior, local brown 

hematite and Port Henry magnetite ores. 
Not in operation March, 19 10. 

Poughkeepsie. — Poughkeepsie fees. (2 stacks), Poughkeepsie, N. Y. 
(Poughkeepsie Iron Co.) 
Not in operation March, 1910. (See Poughkeepsie.) 

Princess. — Princess fee.. Glen Wilton, Va. (Princess Furnace Co.) 
Hot blast, coke, foundry iron, from local limonite. 
Sil. up to 3.0 or 4.0% Phos. 0.60-0.80% Mang. up to 1.0% 

Pulaski. — Pulaski fee., Pulaski, City, Va. (Pulaski Iron Co.) 
Hot blast, coke, foxmdry iron, from local brown ores. 
Sil. 2.0-3.50% Phos. 0.50-0.80% Mang. 0.40-0.70% 

Punxy. — Punxy fee., Punxsutawney, Pa. (Punxsutawney Iron Co.) 
Hot blast, coke, foundry iron, from Lake Superior hematite. 
Sil. 1.0-4.0% Phos. 0.40-0.60% Mang. 0.45-1.60% 

Radford. — Radford Crane fee., Radford, Va. (Va. Iron, Coal & Coke Co.) 
Hot blast, coke, foundry iron, from Va. limonite and mountain ores. 
Sil. 1.5-2.75% Phos. abt. 1.00% Mang. abt. 1.25% 

Rebecca. — Rebecca fees. (2 stacks), Kittanning, Pa. (Kittanning I. 
& S. Mfg. Co.) 
Hot blast, coke, chill east iron, from Lake Superior ores. 
Fdry. Sil. up to 3.0% Phos. 0.40-0.80% Mang. imder 1.0% 

Basic under i.o under 0.50 under i.o 

Mall. 1. 0-1.50 under 0.20 under 1.0 

* Sometimes up to 8.00 per cent. 



Coke and Athracite Irons 649 

Red River. — Helen fee., Clarksville, Tenn. (Red River Furnace Co.) 
Hot blast, coke, from local brown hematite. 
Fdry. Sil. 2.0- 3.0% Phos. abt. 0.80% Mang. abt. 0.65% 
Scotch 3.5- 5.5 abt. 0.80 abt. 0.60 

High Silicon 8.0-12.0 abt. 0.80 abt. 0.40 

Rising Fawn. — Rising Fawn fee., Rising Fawn, Ga. (Southern I. 
& S. Co.) 

Hot blast, coke, iron from red and brown hematites. 
Not in operation March, 1910. 

Roanoke. — West End fee., Roanoke, Va. (West End Furnace Co.) 
Hot blast, coke, foundry iron, from Va. brown hematite. 

Sil. as desired. Phos. 0.75-1.0% Mang. 0.50-1.0% 

Robesonia. — Robesonia fee., Robesonia, Pa. (Robesonia Iron Co. 
Ltd.) 
Hot blast, anthracite and coke, foundry iron, from Cornwall ore. 
Sil. 2.0-3.50% Phos. under 0.04% Mang. abt. 0.10% 

Rockdale. — Rockdale fee., Rockdale, Tenn. (Rockdale Iron Co.) 
Hot blast, coke, iron from Tenn. brown hematite. 
Fdry. Sil. 2.0 -2.75% Phos. abt. 1.40% Mang. abt. 0.25% 

Ferro Phos. 0.07-0.75 17.0-22.0 0.15-0.25 

Rockhill. — Rockhill fees., (2 alt. stacks), Rockhill P. O., Pa. (Rockhill 
Fee. Co.) 
Hot blast, coke, iron from fossil and Lake Superior ores. 
Not in operation March, 19 10. 

Rockwood. — Rockwood fees. (2 stacks), Rockwood, Tenn. (Roane 
Iron Co.) 
Hot blast, coke, foundry iron, from red fossil ore. 
Sil. 1.75-2.75% Phos. abt. 1.40% Mang. abt. 0.50% 

Sampson Strong. — Upson fee., Cleveland, O. (Upson Net Co.) 
Hot blast, coke, foundry iron, from Lake Superior ore. 
Sil. 1.5-1.8% Phos. 0.40-0.60% Mang. 0.60-1.0% 

Sarah. — Sarah fee., Ironton, O. (The Kelley Nail & Iron Co.) 
Hot blast, coke, Bessemer iron, from Lake Superior ore. 

Saxton. — Saxton fees. (2 stacks), Saxton, Pa. (Jos. E. Thropp.) 

Hot blast, coke, foundry iron, from Lake Superior and local brown 

ores. 
Sil. 1.5-3-5% Plios- 0.40-0.90% Mang. 0.50-0.90% 

Scottdale. — Seottdale fee., Scottdale, Pa. (.Scottdale Furnace Co.) 
Hot blast, coke, foundry iron, from Lake Superior ore. 



650 Pig Iron Directory 

Senega. — McKeefrey fee., Leetonia, O. (McKeefrey & Co.) 
Hot blast, coke, foundry iron, from Lake Superior ores . 
Sil. 1.0-2.0% Phos. under 0.20% Mang. 0.40-0.80% 

Sharpsville. — Sharpsville fee., Sharps ville, Pa. (Sharpsville, Fee. Co.) 
Hot blast, coke, mostly Bess, iron, from Lake Superior and New 
York magn. ores. 

Sheffield. — Shemeld f-ces. (3 stacks), Sheffield, Ala. (Sheffield C. & 

I. Co.) 
Hot blast coke, foundry iron, from Alabama and Tennessee brown 

hematites. 
Sil. as desired. Phos. abt. i.o;% Mang. abt. 0.50% 

Sheffield. —B.a,ttie Ensley fee., Sheffield, Ala. (Sloss-Sheffield S. & I. 
Co.) 
Hot blast, coke, foundry iron, from local brown hematite. 
Sil. as desired. Phos. abt. 1.20% Mang. abt. 0.50% 

Shenandoah. — Gem fee., Shenandoah, Va. (Oriskany Ore & Iron Co.) 
Hot blast, coke, foundry iron, from local brown hem. and Lake 

Superior ores. 
Sil. as desired. Phos. 0.40-0.80% Mang. 0.60-1.0% 

Shenango. — Shenango fees. (5 stacks), Sharpsville, Pa. (Shenango 
Fee. Co.) 
Hot blast, coke, basic, chill east iron, from Lake Superior ores. 
Sil. under 1.0% Phos. under 0.05% Mang. 0.70-1.30% 

Sheridan. — Sheridan fee., Sheridan, Pa. (Berkshire Iron Works.) 
Hot blast, anthracite and coke, foundry iron, sand cast, from Corn- 
wall local hematite. 
Sil. 1.0-4.0% Phos. 0.40-0.90% Mang. up to 0.75% 

Silver Creek. — Rome fee., Rome, Ga. (Silver Creek Furnace Co.) 
Hot blast, coke, sand cast, foundry iron, from red and browm hema- 
tite, local. 
Sil. up to 5.0% Phos. under 1.0% Mang. up to 2.0% 

Silver Spring. — Paxton fees. (2 stacks), Harrisburg, Pa. (Central 
I. & S. Co.) 
Hot blast, anthracite and coke, foundry iron, from various ores. 

Sloss. — Sloss fees. (4 stacks), Birmingham, Ala. (Sloss-Sheffield S. 

& I. Co.) 
Hot blast, coke, foundry iron, from red fossil, hard and soft and 

brown hematites. 
Sil. as desired. Phos. abt. 0.75% Ma^ng. abt. 0.40% 



Coke and Anthracite Irons 651 

Soho. — Soho fee., Pittsburg, Pa. (Jones & Laughlin Steel Co.) 
Hot blast, coke, basic and Bes. iron, from Lake Superior ores. 

South Pittsburgh. — So. Pittsburgh fees. (3 stacks). So. Pittsburgh, Tenn. 
(Tenn. Coal, Iron & R.R. Co.) 
Hot blast, coke, mill and foundry, sand east iron, from local hard 

red hematite, and brown hematite from Georgia. 
Sil. up to 3.50%* . Phos. 1.00-1.50% Mang. 0.50-1.50% 

Spritig Valley. — Spring Valley fee.. Spring Valley, Wise. (Spring 
Valley Iron & Ore Co.) 
Hot blast, coke or sometimes charcoal, sand cast iron, from brown 

hematite ore. 
Mall. Sil. 0.80-1.50% Phos. under 0.20% Mang. 1.0-1.5% 

Fdry. 1.5-3.00 under 0.20 1.0-1.50 

Standard. — Standard fee., Goodrich, Tenn. (Standard Iron Co.) 
Hot blast, coke, foundry iron, from local brown hematite. 
Sil. 1.75-4.50% Phos. abt. 0.95% Mang. abt. 0.40% 

Star. — Star fee., Jackson, O. (Star Furnace Co.) 

Hot blast, raw coal and coke, sand cast, Jackson Co. softener, from 

native limonite and block ores. 
Sil. 5.00-12,00% Phos. 0.43-0.80% Mang. abt. 0.70% 

Star &" Crescent. — Rusk fee., Cherokee Co., Pa. (Frank A. Daniels.) 
Hot blast, coke, foundry iron, from local brown hematite and black 

ores. 
Not in operation March, 1910. 

Sterling Scotch. — Iroquois fees. (2 stacks). So. Chicago, 111. (Iroquois 
I. Co.) 

Hot blast, coke, foundry iron, from Lake Superior ores. 

Sil. 2.50-3.0% Phos. 0.30-0.40% Mang. 0.40-0.70% • 

Stewart. — Stewart fee., Sharon, Pa. (Stewart Iron Co., Ltd.) 

Hot blast, coke, sand cast iron, from Lake Superior ores. 

Bess. Sil. 1.0-2.50% Phos. 0.09-0.10% Mang. 0.60-0.80% 

Low Phos. 1.0-2.50 under 0.04 0.20-0.40 

Struthers. — Aurora fee., Struthers, O. (The Struthers Fee. Co.) 

Hot blast, coke, sand east iron, from Lake Superior ores. 

Basic Sil. under 1.00% Phos. under 0.25% Mang. 0.60-1.2% 

Mall. 1. 00-1.50 imdero.2o abt. i.o 

Susquehanna. — (2 stacks) , Buffalo, N.Y. (Buffalo & Susquehanna I. Co.) 

Hot blast, coke, from Lake Superior ores. 

Analysis refused. 

* Sometimes higher. 



Basic up to i.oo 


up to I.O 


Bess. I.O-2.0 


up to O.IO 


Low Phos. 1.0-2.50 


up to 0.035 


Spec. High Mang. i. 0-1.50 


up to 0.80 



652 Pig Iron Directory 

Swede. — Swede fees. (2 stacks), Swedeland, Pa. (Richard Heckscher 
& Sons Co.) 
Hot blast, coke, sand cast iron, from Lake Superior and high grade 
foreign ores. 
Fdry. Sil. up to 3.25% Phos. up to 0.80% Mang. up to 0.80% 

up to 1.25 
up to 2.0 
up to 4.50 
over 1.50 

Sydney. — Mayville fees. (2 stacks), Mayville, Wise. (Northwestern 

Iron Co.) 
Hot blast, coke, foundry iron, from Lake Superior and local 

ores. 
Sil. 1.40-2.50% Phos. 0.60-0.80% Mang. 0.50-1.0% 

Talladega. — Talladega fee., Talladega, Ala. (Northern Ala. C, I., & 
R.R. Co.) 
Hot blast, coke, foundry iron, from native brown ore. 
Not in operation March, 1910. 

Temple. — Temple fee., Reading, Pa. (Temple Iron Co.) 

Hot blast, anthracite and coke, foundry iron, from Lake Superior, 

local hematite, N. J. magnetic and foreign ores. 
Sil. 1.75-3.50% . Phos. 0.60-0.80% Mang. 0.40-0.80% 

The Mary. — Mary fee., Lowellville, O. (The Ohio Iron & Steel Co.) 
Hot blast, coke, Bessemer only, from Lake Superior ores. 

Thomas. — Thomas fee., Milwaukee, Wise. (Thomas Furnace Co.) 
Hot blast, coke, sand cast iron, from Lake Superior ores. 
Mai. Bess. Sil. 1.00-2.00% Phos. 0.10-0.20% Mang. 0.40-1.25% 
Fdry. as desired. 0.15-0.60 0.50-1.25 

Thomas. — (9 stacks.) (The Thomas Iron Co.) 

Hokendauqua fees. (4 stacks), Hokendauqua, Pa. 
Keystone fee. (i stack). Island Park, Pa. 
Lock Ridge fees. (2 stacks), Alburtis, Pa. 
Saucon fees. (2 stacks), Hellertown, Pa. 

Hot blast, anthracite and coke, sand and chill cast iron, from local 
brown hematite, N. J. magnetic and foreign ores. 
Fdry. Sil. as desired. Phos. 0.60-0.90% Mang. abt. 0.50% 

Basic under 1.0% under i.o variable 



Coke and Anthracite Irons 653 

Toledo. — Toledo fees. (2 stacks), Toledo, O. (Toledo Furnace Co.) 
Hot blast, coke, sand cast iron, from Lake Superior ores. 
Mai. Sil. 1.00-2.00% Phos. under 0.20% Mang. 0.60-1.25% 

Basic under I. o under 0.20 0.60-1.25 

Fdry. 1.25-2.25 0.50-0.60 0.60-1.25 

Scotch 2.25-3.00 0.50-0.60 0.60-1.25 

Tonawanda Scotch. — Niagara fees. (2 stacks), N. Tonawanda, N. Y. 
(Tonawanda Iron & Steel Co.) 
Hot blastj coke, foundry iron, from Lake Superior hematite. 
Analysis refused. 

Top Mill. — Top fee., Wheeling, W. Va. (WheeHng Iron & Steel Co.) 
Hot blast, coke, Bess, iron, from Lake Superior ores. 

Topton. — Topton fee., Topton, Pa. (Empire Steel & Iron Co.) 

^ Hot blast, anthracite and coke, foundry iron, from Lake Superior, 
native hematite and magnetite ores. 
Sil. 0.75-3.50% Phos. 0.60-0.90% Mang. 0.50-2.00% 

Trussville. — Trussville fee., Trussville, Ala. (Southern I. & S. Co.) 
Hot blast, coke, sand east, foundry iron from Alabama red and 

Georgia brown hematites. 
Sil. up to 3.50% Phos. 0.90-1.20% Mang. 0.50-1.50% 

Tuscaloosa. — Central fee., Holt, Ala. (Central Iron & Coal Co.) 

Hot blast, coke, sand east, foundry iron from red and brown hema- 
tites. 
Sil. 1.25-2.75% Phos. 0.80-1.0% Mang. .0.50-0.90% 

Tuscarawas. — Dover fee.. Canal Dover, O. (The Penn. I & C. Co.) 
Hot blast, coke, foundry iron, from Lake Superior ores. 

Union. — Buffalo Union fees. (3 stacks), Buffalo, N. Y. (Buffalo 
Union Furnace Co.) 
Hot blast, coke, foundry scotch iron, from Lake Superior ores. 
Sil. 1.75-2.50% Phos. 1.20-1.50% Mang. 0.50-1.0% 

Upson Scotch. — Upson fee., Cleveland, O. (Upson Nut Co.) 
Hot blast, coke, foundry iron, from Lake Superior ores. 
Sil. 2.0-3.0% Phos. 0.40-0.60% Mang. 0.60-0.90% 

Vatiderhilt. — Vanderbilt fees. (2 stacks), Birmingham, Ala. (Birm- 
ingham C. & I. Co.) 
Hot blast, coke, foundry iron, from local hematites. 
Sil. up to 4.00% Phos. under 1.00% Mang. 0.40-1.00% 



654 Pig Iron Directory 

Vesta. — Vesta fee., Watts, Pa. (Susquehanna Iron Co.) 

Hot blast, anthracite and coke, foundry iron, from local hematites 

and magnetites. 
Not in operation March, 19 lo. 

Victoria. — Victoria fee., Goshen, Va. (The Goshen Iron Co.) 

Hot blast, coke, foundry and forge iron, from brown hematite from 

Rich Patch mines. 
Sil. as desired. Phos. 0.40-0.80% Mang. 1.0-1.50% 

Viking. — Same as Carbon, which see. 

Warner. — Cumberland fee., Dickson Co., Tenn. (Warner Iron Co.) 
Hot blast, coke, foundry iron, from local red and brown hematite. 
Sil. 2.0-2.75% Phos. abt. 1.60% Mang. abt. 0.40% 

Warwick. — Warwick fees. (3 stacks), Pottstown, Pa. (Warwick I. & 
S. Co.) 
Hot blast, coke, machine cast foundry iron, from Lake Superior, 

N. Y., New Jersey, and foreign ores. 
Sil. 1.0-3.0% Phos. 0.40-0.80% Mang. 0.40-0.80% 

Watts. — Watts fees. (2 stacks), Middlesborough, Ky. (Va. Coal & 
Coke Co.) 
Hot blast, coke, foundry iron, from native ores. 
Sil. 1.50-2.75% Phos. abt. 0.45% Mang. abt. 0.20% 

Wellston. — Wtnston fees. (2 stacks), Wellston, O. (Wellston S. & 
I. Co.) 
Hot blast, coke, sand cast iron, from Lake Superior ores. 
Str. fdry. Sil.- 1.50-1.75% Phos. 0.18-0.20% Mang. 0.60-0.90% 
Mall. 0.60-2.00 under 0.20 0.40-1.00 

Wharton. — Wharton fees. (3 stacks), Wharton, N. J. (Joseph Whar- 
ton.) 
Hot blast, coke, occasionally some anthracite, from N. J. mag., N. Y. 
and Lake Superior hematites. 

Wickwire. — Wickwire fee., Buffalo, N. Y. (Wickwire Steel Co.) 
Hot blast, coke, basic iron, from Lake Superior ores. 

Williamson. — Williamson fee., Birmingham, Ala. (Williamson Iron 
Co.) 
Hot blast, coke, iron from red fossil, and brown hematite. 
Woodstock. — Woodstock fees. (2 stacks), Anniston, Ala. (Woodstock 
I. Wks., Inc.) 
Hot blast, coke, foundry iron, from local brown hematite. 
Sil. 1.50-5.00% Phos. abt. 1.15% Mang. 0.80-1.25% 



Charcoal Irons 655 

Woodward. — Woodward fee., Woodward, Ala. (Woodward Iron Co.) 
Hot blast, coke, foundry iron, from local red fossil ores. 
Sil. 1.0-3.0% Phos. abt. 0.80% Mang. abt. 0.30% 

Zenith. — Zenith fee., W. Duluth, Minn. (Zenith Furnace Co.) 
Hot blast, coke, iron, from Lake Superior ores. 
Bess. Sil. 1.00-2.00% Phos. 0.08-0.10% Mang. under 1.0% 

Mall. 1.00-2.00 under 0.2 0.80-1.20 

Fdry. 1.50-5.00 under 0.20 over 0.60 

Zug. — Detroit, Mich. (Detroit Iron & Steel Co.) 

Hot blast, coke, foundry iron, from Lake Superior ores. 



Charcoal Irons 

Aetna. — Aetna, Ala. (J. J. Gray.) 

Hot or cold blast, charcoal, car wheel iron, from local brown hema- 
tite. 
Not in operation March, 19 10. 

Alamo. — Quinn fee., Gadsden, Ala. (Quinn Furnace Co.) 

Hot blast, charcoal, foundry iron, from local red and brown hema- 
tite. 
Not in operation March, 19 10. 

Anchor. — Oak Hill, O. (Jefferson Iron Co.) 

Warm blast, ehafcoal, strong foundry iron, from native limestone 

and block ores. 
Sil. abt. 2.26% Phos. abt. 0.87% . Mang. abt. 0.51% 

Antrim. — Antrim fee., Mancelona, Mich. (Superior Charcoal Iron Co.) 
Hot blast, charcoal, foundry iron, from Lake Superior ores. 
Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70% 

Berkshire. — Cheshire fee., Cheshire, Mass. (Berkshire Iron Works.) 
Warm blast, charcoal, foundry iron, from local red and brown hema- 
tite. 

Berlin. — Glen Iron fee.. Glen Iron, Pa. (John T. Church.) 
Cold blast, charcoal, iron from local fossil, and hematite. 
• Sil. 1.0-1.5% Phos. 0.50-0.65% Mang. 0.40-0.60% 

Bloom. — Bloom Switch, O. (The Clare Iron Co.) 

Hot blast, charcoal, foundry iron, from local hematite. 
Not in operation March, 1910. 



656 Pig Iron Directory 

Blue Ridge. — Tallapoosa fee., Tallapoosa, Tenn. (Southern Car Wheel 
Iron Co.) 
Cold and warm blast, charcoal, iron from brown hematite. 

Phos. 0.18-1.50% Mang. up to 2.0% 

Buckhorn. — Olive fee., Lawrence Co., 0. (McGugin Iron & Coal 
Co.) 
Hot or cold blast, charcoal iron, from native limestone ore. 
Not in operation March, 19 10. 

Cadillac. — Cadillac fee., Cadillac, Mich. (Mitehell-Diggins Iron Co.) 
Hot blast, charcoal iron, from Lake Superior ores. 
Sil. up to 2.50% Phos. 0.16-0.20% Mang. up to 1.0% 

Center. — Superior P. O., O. (The Superior Portland Cement Co.) 
Charcoal iron, from native limestone. 
Not in operation March, 1910. 

Champion. — Manistique, Mich. (Superior Charcoal Iron Co.) 
Warm blast, charcoal, foundry iron from Lake Superior ores. 
Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70% 

Cherokee. — Cherokee fee., Cedartown, Ga. (Alabama & Georgia Iron 

Co.) 
Hot blast, charcoal, sand cast, strong foundry iron, from brown 

hematite. 
Sil. up to 2.50% Phos. 0.35-0.70% Mang. 0.30-1.60% 

Chocolay. — Chocolay fee., Chocolay, Mich. (Lake Superior Iron & 
Chemical Co.) 
Warm blast, charcoal iron, from Lake Superior ores. 
Fdry. Sil. up to 2.0% and over Phos. 0.17-0.22% 

.Car Wheel 0.05-2.0 and over 0.17-0.22 

Mall. 0.17-0.22 

Mang. up to 0.65% and over 

0.30-0.65 and over 
0.30-0.65 and over 

Copacke. — Copacke Iron Works, N. Y, (Copaeke Iron Works.) 
Cold and warm blast, charcoal iron, from N. Y, ores. 
Not in operation March, 19 10. 

Dover. — Bear Spring fee., Stewart Co., Tenn. (Dover Iron Co.) 
Cold blast, charcoal, foundry iron, from local brown hematite. 
Sil. 0.40-2.0% Phos. abt. 0.40% Mang. abt. 0.25% 



Charcoal Irons 657 

Elk Rapids. — Elk Rapids, Mich. (Superior Charcoal Iron Co.) 

Hot blast, charcoal, pig for car wheels and mall., from Lake Superior 

ores. 
Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.36-0.70% 

Excelsior. — Carp fee., Marquette, Mich. (Superior Charcoal Iron Co.) 
Warm blast, charcoal iron, from Lake Superior ores. 
Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.20-0.70% 

Gertrude. — Maysville fees. (2 stacks), Maysville, Wise. (Northwest 
Iron Co.) 
Hot blast, charcoal, foimdry iron, from Lake Superior and local 

ores. 
Sil. 2.50% and over Phos. 0.60-0.80% Mang. 0.50-1.00% 

Glen Iron. — Glen Iron fee.. Glen Iron, Pa. (John T. Chmrch.) 
Cold blast, charcoal iron, from local fossil and hematite. 
Sil. up to 1.00% Phos. 0.70-1.25% Mang. 0.60-1.50% 

Hecla. — Hecla fee., Milesburg, Pa. (The McCoy-Linn Iron Co.) 
Cold blast, charcoal, foundry iron, from Nittany Valley hematite. 
Sil. 0.65-1.25% Phos. abt. 0.30% Mang. 0.15-0.25% 

Hecla. — Hecla fee., Ironton, O. (Hecla Iron & Mining Co.) 
Cold or warm blast, charcoal, foundry iron, from local ore. 

Hematite. — Center fee.. Center, Ky. (White, Dixon & Co.) 
Cold blast, charcpal, foundry iron, from local hematite. 
Sil. 0.50-1.40% Phos. 0.25-0.39% Mang. 0.20-0.25% 

Hinkle. — Ashland fee., Ashland, Wise. (Lake Superior Iron & Chem- 
ical Co.) 
Warm blast, charcoal iron, from Lake Superior ores. 
Sil. up to 3.00% Phos. 0.10-0.18% Mang. to 0.70% and over 

Jefferson. — Jefferson fee., Jefferson, Tex. (Jefferson Iron Co.) 
Hot blast, charcoal iron, from local brown hematite. 
Not in operation March, 1910. 

Liberty 1^12. — Liberty fee., Shenandoah Va. (Shenandoah I. & C. 
Co., Va.) 
Warm blast, charcoal iron, from brown hematite. 

Marquette. — Pioneer fee., Marquette, Mich. (Superior Charcoal Iron 
Co.) 
Hot blast, charcoal, foundry iron, from Lake Superior ore. 
Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70% 



658 Pig Iron Directory 

Michigan. — Newberry fee., Newberry, Mich. (Superior Charcoal Iron 
Co.) 
Warm blast, charcoal iron, from Lake Superior ores. 
Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70 

Muirkirk. — Muirkirk fee., Muirkirk, Md. (Charles E. Coffin.) 
Warm blast, charcoal iron, from local carbonate ores. 
Sil. 0.70-2.50% Phos. 0.25-0.30% Mang. 0.80-2.50% 

Olive. — Olive fee., Lawrence Co., O. (The McGugin I. & C. Co.) 
Hot or cold blast, charcoal iron from native limestone ores. 

Pine Lake. — Boyne City fee., Boyne City, Mich. (Superior Charcoal 
Iron Co.) 
Hot blast, charcoal iron, from Lake Superior ores. 
Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70% 

Pioneer. — Pioneer fee., Gladstone, Mich. (Superior Charcoal Iron Co.) 
Warm blast, charcoal iron, from Lake Superior ores. 
Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70% 

Reed Island. — Reed Island fee.. Reed Island, Va. (Va. Iron, C. & C. Co.) 
Cold blast, charcoal iron, from local limonite. 

Richmond. — Richmond fee., Berkshire Co., Mass. (Richmond Iron 
Works.) 
Warm blast, charcoal iron, from local brown hematite. 
Sil. up to 2.00% Phos. 0.28-0.35% Mang. up to 0.44% 

Rock Run. — Rock Run fee., Rock Run, Ala. (The Bass Foundry & 

Machine Co.) 
Warm blast, charcoal iron for chill rolls, ear wheels, strong eastings, 

from local brown hematite. 
Sil. 0.30-2.25% Phos. 0.30-0.50% Mang. 0.40-1.00% 

Rome. — Rome fee., Rome, Ga. (Silver Creek Furnace Co.) 

Warm blast, charcoal iron, from local red and brown hematites. 
Sil. 1.75-2.25% Phos. 0.35-0.60% Mang. 0.50-0.80% 

Round Mountain. — Round Mt. fee,. Round Mt., Ala. (Round Moun- 
tain Iron & Wood Ale. Co.) 
Cold blast, charcoal iron, from local red hematite. 
Not in operation March, 1910. 
Salisbury. — Canaan fees.. East Canaan, Conn. (2 stacks). (Bamum 
Richardson Co.) 
Warm blast, charcoal iron, from Salisbury brown hematite, sand 

cast. 
Sil. 1.32-1.92% Phos. abt. 0.30% Mang. 0.50-1.0% 



Charcoal Irons 659 

Salisbury Chatham. — Chatham fee., Chatham, N. Y. (Union Iron & 
St. Co.) 
Charcoal iron. 

Shelby. — Shelby fee., Shelby, Ala. (Shelby Iron Co.) 

Warm blast, charcoal iron, from local brown hematite. 

Sil. 0.15-2.25% Phos. 0.30-0.50% Mang. 0.50-0.80% 

Sligo. — Sligo fee., Sligo, Mo. (Sligo Furnace Co.) 

Hot blast, charcoal iron, from local blue specular and red ore. 

Spring Lake. — Fruitport fee., Fruitport, Mich. (Spring Lake Iron 
Co.) 
Hot blast, sand cast, charcoal iron, from Lake Superior ores. 
Sil. up to 2.50% Phos. 0.16-0.20% Mang. up to 1.0% 

Spring Valley. — See under Coke Irons. 

Tassie Bell. — Tassie Bell fee.. Rusk, Tex. (New Birm. Devel. Co.) 
Hot blast, charcoal iron, from local brown hematites. 
Not in operation March, 1910. 

White Rock. — Smyth Co., Va. (Lobdell Car Wheel Co.) 

Warm and cold blast, charcoal iron, from local brown hematite. 
All used by the Company. 

Wyebrooke. — Isabella fee., Wyebrooke, Pa. (W. M. Potts.) 

Cold blast, charcoal iron, from local magnetic and hematites and 

foreign and Lake Superior ores. 
Not in operation March, 1910. 



AUTHORITIES 



BOLAND, S. 

Buchanan, J. S. 
Buchanan, Robert. 
Byron, T. H. 

" Castings. " 
Carpenter, H. A. 
Carr, W. N. 
Christopher, J. E. 
Chrystie, J. 
Cheney, F. R. 
Colby, A. L. 
Cook & Hailstone. 
Cook, E. S. 
Crobaugh, F. L. 
Custer, E. A. 
Cunningham, R. P. 

De Clercy, Jules. 
Dickinson, W. E. 
DiLLER, H. E. 

Fay, a. E. 
Field, H. E. 
Firmstone, F. 
Franklin, B. A. 
"The Foundry." 

Gilmore, E. B. 
Golden, E. B. 

Hall, J. L. 
Hatfield, W. 
Hawkins, D. S. 
Hiones, a. H. 
Holmes, J. A. 



Hooper, G. K. 
Howe, Prof. H. M. 
Hyndman, N. p. 

"Iron Age." 

"Iron Trade Review." 

Jewett, L. C. 
Johnson, F. 
Johnson, J. E., Jr. 

Kane, W. H, 
Keep, W. J. 
Kent, Wm. 
Kirk, E. 
Knoppell, C. E. 

Lane, H. M. 
Ledebur, Prof. A. 
Long, A. T. 

LONGMUIR, P. 

Loudon, A. M. 

Marshall, S. P. 
May, W. J. 

McWilliams & Longmuir. 
McGahey, C. R. 
"Mechanics." 
Moldenke, Dr. R. 
mumford, e. h. 
Murphy, Jos. A. 

Nagle, a. F. 

Outerbridge, a. E. 



660 



Authorities 



66i 



Palmer, R. H. 
Pierce, E. H. 
Porter, Prof. J. J. 
Probert, R. H. 
Putnam, E. H. 

Rankine, Prof. W. J. M. 
RiES, Prof-. H. 
Raup, p. R. 
Recketts, Prof. P. C. 
Robertson, J. S. 
Rogers, S. M. 
RoTT, Prof. Carl 
Rossi, A. G. 

Sadlier, J. G. 
Saunders, W. M. 
Sameur, Prof. A. 
Scott, W. G. 
Shed, N. W. 



SiSSONS, C. W. 
Stahlund, Eissen. 
Stickle, F. W. 
Stupakoff, S. H. 
Stead, J. E. 
Sleeth, S. D. 
Stoughton, Prof. B. 

Trautwine, J. C. 
Turner, Prof. T. 
Taylor, E. M. 

West, Thos. D. 
Whitehouse, J. S. 
Whitney, A. W. 
Williams, A. D. 

W ANGLER, J. 

WuEST, Prof. F. 
Wylie, C. 



INDEX 



Abbreviations and signs, v. 

Acceleration of falling bodies, 191-93. 

Accounts, See Foundry accounts. 

Acid open hearth, 417, 419, 422. 

Acid-resisting-castings, mixture for, 
276. 

Addition in algebra, 8. 

Agricultural castings, average of five 
meltings, 459. 

Agricultural machinery, mixtures for, 
276. 

Air, weight of, for combustion, 204; 
properties of , 215-18; required for 
combustion of one pound each 
of coke and coal, 444; loss in 
pressure and horse power from 
friction in pipes, 447. 

Air, compressed, horse power required 
for, 217-18. 

Air cylinders, mixture for, 276 

Air furnace, American, 391. 

Algebra, 7-15. 

Alligation, 5. 

Alloys, 222-27. 

Alviminvun, properties of, 266; in- 
fluence of, in cast iron, 266-67. 

Aluminum bronze, 226. 

American Foundrymen's Association, 
See Foundrymen's Association. 

American Steel & Wire Co., gauge of 
sizes, 146. 

Ammonia cyUnders, mixture for, 276. 

Analysis, mixing iron by, 274-89. 

Anchors, gaggers and soldiers, 523-24. 

Angle, problems of the, 17-18. 

Angles, approximate measurement of, 
115-16. 

Annealing boxes, mixtures for, 277. 

Anneahng-oven equipped for gas. 392. 

Annealing steel castings with micro- 
graphs, 400-1. 

Anthracite coal, 425. 

Antimony, alloys containing, 227. 



Apothecaries' or wine measure, 38. 
Apothecaries' weight, table of, 36. 
Appliances about cupola, 462-67. 
Arithmetic, 1-7. 
Arnold, Prof. J. O., on carbon in steels, 

241, 347; mechanical properties 

of normal steels, 396. 
Atmosphere, pressure of, at various 

readings of barometer, 216. 
Authorities, 660-61. 
Automobile castings, mixtures for, 277. 
Avoirdupois weight, table of, 36. 

B.t.u. = British thermal unit, 207. 

Babbitt metal, 227. 

Baby (Robert) converter, the, 397. 

Balls for ball mills, mixture for, 277. 

Band and hoop iron weights, 121- 
22. 

Barometric readings, pressure of at- 
mosphere at various, 216; corre- 
sponding with different altitudes, 
217. 

Bars of wrought iron, weight and 
areas of square and round, 136- 
39- 

Basic open hearth, 418, 419, 423. 

Bauxite, fire bricks of, 436. 

Beams, transverse strength of, for- 
mulas for, 188-90. 

Bearing-metal alloys, 226. 

Bed-plates, mixture for, 277. 

Belt velocity, tables oi, 229-30. 

Belting, formulas for, 227-28. 

Benjamin, Charles H., strength of 
materials, 213-14. 

Bessemer process, the, 396. 

Binder bars, 505. 

Binders, See Agricultural machinery. 

Birmingham gauge for sheet metals 
except steel and iron, 120. 

Black heart malleable cast iron, 382- 
85. 



663 



664 



Index 



Blast, the, in the cupola, 446-47 ; loss 

of air pressure from friction in 

pipes, 447. 
Blast pipes for pressure blowers, 

tables of, 450. 
Blow-holes, trouble with, 316; in 

steel, 398. 
Blowers, pressure, for cupolas, tables 

of, 448-49. 
Board and timber measure, 44. 
Board measure, table of, 91-92. 
Bod stick, the, 463-64. 
Boiler castings, mixture for, 277. 
Boiling points at gea level, 204; at at- 
mospheric pressure, 210. 
Bolt end's and lag screws, 158. 
Bolt heads and nuts, weights of, 159. 
Bolts and nuts, U. S. standard, 150-51. 
Bolts, machine, weight of, per 100, 

155-56; list prices, 157. 
Borings and turnings, melting, 293; 

per cent of, 322. 
Box strapping, 236. 
Brake shoes, mixture for, 287. 
Brass, fillets of, areas and weights of, 

145- 
Brass foundries, alloys in use in, 223. 
Brass, moulding sand for, 472. 
Brass, sheet and bar, weight of, 144. 
Brass tubes, seamless drawn, 167-69. 
Brass wire and plates, weight of, 143. 
Breaking loads, formula for, 301; 

ratio of tensile strength to, 10 to i, 

302. 
Breast of cupola, 440-41. 
Buffalo steel pressure Blowers, 449. 

Cables, See Chains and cables. - 
Cables, transmission or standing, 

179- 

Calorie, French thermal unit, 207. 

Cap screws, 161. 

Car castings, mixtures for, 278. 

Car wheel iron test bars, moduli of 
rupture of, 300. 

Car wheels, qualities of iron for, 275; 
mixtures for, 278; specifications 
for, 3SO-5S- 

Carbon and iron, forms of combi- 
nation of, 313. 

Carbon, combined, See Cementite. 

Carbon content in steel, 395. 



Carbon, properties of, 252-53; in- 
fluence of, as constituent of cast 
iron, 253-54; loss or gain of, in 
remelting, 254-56. 

Carbon, total, per cent, 308, 310; in 
micrographs, 311; ways of re- 
ducing, 315—16; for elasticity, 
323; reduced for hardness, 328; 
high to decrease shrinkage, 332; 
high aids fluidity, 335; for re- 
sistance to heat, 337-38; for 
high permeability, 340; for re- 
sistance to corrosion, 341; de- 
termination of, 379-80. 

Carpenter shop and tool room, 562. 

Carr, W. M., open-hearth methods 
for steel castings, 411-16. 

Carrier, W. H., on foundry heating 
and ventilating, 582-86. 

Cast iron, constituents of, standard 
methods for determining, 377-80: 
Silicon, 377-78; sulphur, 378; 
phosphorus, 378; manganese, 
379; total carbon, 379-80; graph- 
ite, 381. 

Cast iron, effect of structure of, upon 
its physical properties, 306-14; 
microscopic evidence, 308-12; 
Prof. Porter on, 312-14. 

Cast iron, fillets of, areas and weights 
of, 145. 

Cast iron, influence of chemical con- 
stituents of, 252-72: Carbon, 252- 
56; silicon, 256-60; sulphur, 
260-63; phosphorus, 263-64; 
manganese, 265-66; aluminum, 
266-67, nickel, 267; titanium, 
267-68; vanadium, 268-70; ther- 
mit, 270; oxygen, 270-71; ni- 
trogen, 271—72. 

Cast iron, mechanical analysis of, 
see Mechanical analysis. 

Cast iron, weight of a superficial foot 
of, 570. 

Casting, direct, 562. 

Casting properties of iron, 343-45- 

Castings,, mixtures for various classes 
of, 273-74; (alphabetical) 276-87; 
amounts of different irons to be 
used found by percentage, 287-89. 

Castings, qualities of iron necessary 
for different grades of, 275. 



Index 



665 



Castings, shrinkage of, per foot, 234. 

Castings under pressure, 562. 

Castings, weight of, determined from 
weight of patterns, 569-70; for- 
mulas for finding, 570-76. 

Cement mortar, tensile strength of, 
215. 

Cementite (combined carbon), 241; 
in micrographs, 308-1 1 ; physical 
characteristics of, 313; per cent 
combined carbon, 315, 319-20, 
323; causes hardness, 324-29; 
for fusibility, 332-34; low for 
fluidity, 335; for resistance to 
heat low, 337-38; low for per- 
meability, 340; in micrographs, 
346-49- 

Center of gravity, 195-97. 

Centigrade to Fahrenheit, equiva- 
lent temperatures, 211-12. 

Centismal years, 43. 

Centrifugal castings, 561-62. 

Centrifugal force, 215. 

Chain end link and narrow shackle, 
174. 

Chain hooks, proportions for, 172. 

Chains and cables, U. S..Navy stand- 
ard, 173. 

Chaplets, 528-36; peerless perforated, 
530; double head, 531-32; 
wrought-iron, 533-35- 

Charcoal iron, 250. 

Charcoal pig irons, directory of, 655-59. 

Charging cupolas, 452-54. 

Charging floor, the, 453-54- 

Charpy & Grenet's experiments on 
irons, 383. 

Chemical analyses of cast iron, 315-49 : 
Strength, 315-22; elastic prop- 
erties, 322-29; shrinkage, 329- 
32; fusibility, 332-34; fluidity, 
334-35; resistance to heat, 335- 
38; electrical properties, 338-40; 
resistance to corrosion, 340-42; 
resistance to wear, 342; coeffi- 
cient of friction, 342-43; casting 
properties, 343-45; micro-struc- 
ture, 345-49- 

Chemical analyses of test bars, 308- 
12; micrographs, 308-11; forms 
of combination of iron and car- 
bon, 313. 



Chemical constituents of cast iron, 
influence of the (W.- G. Scott), 
252. 

Chemical reactions in the cupola, 443- 

Chilled castings, mixtures for, 274, 
275, 278. 

Chilled iron defined, 326-28. 

Chilled roll (furnace) iron test bars, 
moduli of rupture of, 299. 

Chills, mixture for, 278. 

Chipping and grinding, 566. 

Chords for spacing circle, 89-90. 

Chords of arcs from one to ninety de- 
grees, 88. 

Circle, length of chord for spacing, 
89-90. 

Circle, problems of the, 15, 18-20; 
ratio of circumference to di- 
ameter, 28; area of, 28. 

Circles, areas and circumferences of, 
for diameters from -^q to 100, by 
tenths, 70-79; rules to compute 
larger, 79. 

Circles, areas and circumferences of, 
for diameters in units and eighths, 
64-69. 

Circular arcs, table of, 80-82. 

Circular arcs, table of lengths of, to 
radius i, 82-84. 

Circular measure, 43. 

Circular segments, table of areas of, 
84-87. 

Cisterns and tanks, number of bar- 
rels in, loo-i. 

Clamps, 506. 

Clarke, D. K., formula for extreme 
fibre stress, 304; volume, den- 
sity and pressure of air at vari- 
ous temperatures, 216. 

Cleaning room, the, 563-68; tumblers, 
563-66; chipping, grinding, the 
sand blast, 566; pickHng, 567; 
hydrofluoric acid, 568. 

Clout nails, tinned, 536. 

Coach screws, gimlet points, 159. 

Coke and anthracite pig irons, direc- 
tory of, 635-55. 

Coke, 425-29: Analyses of various 
kinds of, 425-26; by-product 
coke, 426-27; effect of atmos- 
pheric moisture upon, 427; 



666 



Index 



specifications for, by R. Mol- 
denke, 428-29 ; number of pounds 
of iron melted by one pound of, 

444-45- 
Colby, A. L., influence of the mould 

upon pig iron, 249. 
Coleman, J. J., heat-conducting power 

of covering materials, 210. 
Collars and couplings, mixture for, 278. 
Combining equivalents, 204. 
Conductivity of metals, 206, 209. 
Cone, the, 32-33- 
Contraction or shrinkage, 329-32. 
Converter linings, 404-5; practice, 

405-9- 

Converter steel, cost of, 420, 421. 

Converters, the Baby (Robert) and 
Tropenas, 397. 

Cook, E. S , on different results from 
two irons of same chemical com- 
position, 330-32. 

Cook, F. J., and G. Hailstone, micro- 
scopic evidence why similar irons 
have different relative strengths, 
306-12, 317-19- 

Cooling, influence of rate of, 318. . 

Cope, formula to find weight re- 
quired on a, to resist pressure of 
molten metal, 575. 

Copper and tin, alloys of, 222. 

Copper and zinc, alloys of, 223. 

Copper-nickel alloys, 224. 

Copper, round bolt, weight of, per 
foot, 144. 

Copper, tin and zinc, useful alloys of, 
225. 

Copper tubes, seamless drawn, 167-69. 

Copper wire and plates, weight of, 143. 

Core machines, 499. 

Core mixtures, 480-86. 

Core ovens, 492-95. 

Core plates and driers, 498-99. 

Core room and appurtenances, 492- 
500: The oven, 492-96; core 
oven carriages, 496; mixing ma- 
chines, sand conveyors, rod 
straighteners, wire cutter, 497; 
sand driers, 498; core plates and 
driers, 498-99; core machines, 
mould-machines, cranes and 
hoists, 499-500. 

Core sand with analysis, 479-80. 



Corrosion, resistance to, 340-42. 

Corrugated iron roofing, weight of, 
141. 

Cosine, 107. 

Cotters, steel spring, 164. 

Cotton machinery, mixture for, 278. 

Covering materials, heat-conducting 
power of, 210. 

Cranes and hoists for core room, 499- 
500. 

Cranes for cupola service, 466. 

Cranes for moulding room, 502. 

Crucible castings, 423. 

Crusher jaws, mixture for, 278. 

Cube of a whole number ending with 
ciphers, to find, 56. 

Cube root, 4-5. 

Cube root of large number not in 
table, to find, 62-63. 

Cube roots of numbers from 1000 to 
10,000, 57-61. 

Cubes and cube roots of numbers 
from .01 to 1000, tables of, 46-56. 

Cupola, construction of the, 437-52: 
Five zones, 437, 442-43; the 
lining, 437-39; tuyeres, 439-40; 
the breast, 440-41; sand bottom, 
441; chemical reactions in ordi- 
nary, 443-45; wind box, 445; 
builders' rating, 446; blowers for 
the blast, 446-49; diameter of 
blast pipes, 450-51; dimensions, 
etc., of, 451-52. 

Cupola appliances, 462-67: Ladles, 
462-65; tapping bar, 463; bod 
stick, 464-65-; cranes, 466; spill 
bed, 466; gagger mould, 467; 
rake, 467. 

Cupola charging and melting, 452-61: 
The charging floor, 453-54; 
tables of meltings and losses, 455- 
61; melting ratio, 461. 

Cupola makers, best known, 446. 

Custer, Edgar A., on permanent 
moulds, 559-61. 

Cutting tools, mixture for, 278. 

Cylinder, the, 32. 

Cylinder iron test bars, moduli of 
rupture of, 300. 

Cylinders or pipes, contents of, 102-3. 

Cylinders, locomotive, mixtures for, 
273, 282; specifications for, 355. 



Index 



667 



Cylinders, marine and stationary, 
mixtures for, 273; see also Cylin- 
ders, 279. 

Cylinders, solid and hollow iron, for- 
mulas for finding weigiit of, 570- 
71. 

Decimal equivalents of parts of one 

inch, 6. 
Deflections, table of, 183-85. 
Delta metal, 225. 
Diamond polishing wheels, mixture 

for, 279. 
Dies for drop hammers, mixture for, 

279- 
Diller, H. E., tests of use of steel scrap 

in mixtures of cast iron, 290-91; 

on malleable cast iron, 390-91. 
Division in algebra, 10. 
Dry measure, British Imperial, see 

Liquid and dry measures, British 

Imperial, 39-40. 
Dry measure, table of U. S., 39; 

weights of, 39. 
Dynamo and motor frames, mixtures 

for, 279. 
Dynamo frame iron test bars, moduli 

of rupture of, 299. 

Earth, measurements of, and on the, 
238-39- 

Eccentric straps, 279. 

Elastic properties, 322-23. 

Elasticity, modulus of, 181; table of 
moduli, 182-83. 

Electric furnace steel, cost of, 424. 

Electrical and mechanical units, equiv- 
alent values of, 220-21. 

Electrical castings, mixture for, 279. 

Electrical properties, 338-40. 

Elimination, 12-13. 

Ellipse, construction of an, 21-22; 
circumference and area of an, 
_ 29. 

Ellipse, solid iron, formula to find 
weight of a, 571. 

Engine castings, mixtures for, 279. 

Equations, quadratic, 14-15. 

Equations, simple, 11-14; solution 
of, 12. 

Expansion, lineal, for solids, 205. 

Eye bolts, table for, 175. 



Facings, 486-87 ; graphite facing and 
analyses, 488-91. 

Factors, useful, 44-45. 

Fahrenheit to Centigrade, equivalent 
temperatures, 211— 12. 

Falling bodies, acceleration of, for- 
mulas and table, 191-92. 

Fans and blowers, 280. 

Farm implements, mixture for, 280. 

Fe-C-Si, influence of, on cast iron, 
315, 320.^ 

Ferrite, pure iron, 241, 347. 

Field, H. E., on carbon and silicon in 
pig iron, 253. 

Fillet, cast iron straight, formula to 
find weight of a, 574; of a cir- 
cular, 575-76. 

Fillets of steel, cast iron and brass, 
areas and weights of, by E. J. 
Lees, 145. 

Fire brick, 236. 

Fire brick and fire clay, 434-36; 
analyses, 434-35; ganister, 435; 
fine sand, 435; magnesite, 436; 
bauxite, 436. 

Fire clays, analysis of, 237. 

Fire pots, mixture for, 280. 

Flanged fittings, cast iron, 232. 

Flasks, 506-18: Wooden cope and 
drag, 506-9; iron, 510-14; ster- 
ling steel, 515-17; snap, 517-18; 
slip boxes, 519; in machine 
moulding, 547-50- 

Flat rolled iron, see Iron, flat rolled. 

Flat rolled steel, see Steel, flat rolled. 

Floor plates, grate bars, etc., average 
of two meltings, 460. 

Fluidity, factors governing, 334-35- 

Fluxes, 429-34: Limestone and fluor 
spar, 430-31; analyses of slags, 
432-33. 

Flywheel, cast iron, formulas to find 
weight of a, 572-73. 

Foot, inches to decimals of a, 6. 

Foot pound, the unit of work, 45. 

Forces, parallelogram and parallelopi- 
pedon of, 192. 

Foundry accounts, 587-632: Foundry 
requisition, 588-89; pattern card, 
589-90; pig iron card, and book, 
59o> 591; coke card, 591; heat 
book, 592-96; cleaning room re- 



668 



Index 



port, 597; foundry reports, 598- 
600; monthly expenditure of 
supplies, 601-4; monthly com- 
parison of accounts, 605-7; ^.n- 
nual comparison, 608-10; chart 
of transmission of orders, 611-12; 
foundry costs (B. A. FrankHn), 
612-25; successful foundry cost 
system (J. P. Golden), 625-32. 

Foundry cost system, a successful 
(J. P. Golden), 625-32. 

Foundry costs (B. A. Franklin), 612- 
25; outline of scheme, 612-13. 

Foundry pig iron, see Pig iron. 

Foundrymen's Association, American, 
standard specifications for found- 
ry pig iron, 246-48; table of 
mixtures for various castings, 
275-76; report of committee on 
test bars, 294-306. 

Fractions, products of, expressed in 
decimals, 7. 

Fracture, of pig iron, index of com- 
position, 273. 

Franklin, B. A., foundry costs, 612- 
25; outline of scheme, 612-13. 

Frick, Louis H., dimensions of stand- 
ard wrot pipe, 167. 

Friction clutches, mixture for, 280. 

Friction, coefficient of, 215, 342-43. 

Frustrum of a cone, 33; center of 
gravity of a, 196. 

Frustrum of a hexagonal pyramid of 
cast iron, formula to find weight 
of, 574- 

Frustrum of a pyramid, 30-31. 

Fuels, foundry, 425-29: Anthracite 
coal, 425; coke, 425-29. 

Furnace castings, mixture for, 280. 

Furnace temperatures, 206. 

Fusibility, or melting point, 332-34. 

Gagger mould, 467. 

Gaggers, 524. 

Galvanized sheet iron, weight of, 141. 

Ganister, composition of, 435. 

Gas engine cylinders, mixture for,. 280. 

Gases, specific gravity of, 197. 

Gates, tables of areas of, 524-25; top 

pouring, 526; whirl, 527; "cross" 

skim, 527; horn, 527. 
Gears, mixtures for, 280-81. 



Geometry, plane, problems in, 15-24. 

German silver, 224. 

Golden, J. P., a successful foundry 
cost system, 625-32. 

Grain structure of cast iron, 329. 

Graphite, shown in micrographs, 308- 
II, 346-48; physical character- 
istics of, 313; per cent of, 315-17, 
330-31; size of flakes in relation 
to strength, 317-19; per cent of, 
for fusibility, 333-34; for resist- 
ance to heat, 337-38; low, for 
friction, 342. 

Graphite facing, with analyses, 488-91. 

Grate bars, mixture for, 281. 

Gray iron castings, specifications for, 
296-97. 

Grinding machinery, mixture for, 281. 

Grinding wheel speeds, table of, 231. 

Guldin's theorems, 34. 

Gun carriages, mixture for, 281. 

Gun iron, mixture for, 281. 

Gun iron test bars, moduli of rupture 
of, 300. 

Gyration, radius of, 197. 

Hailstone, G., see Cook, F. J. 

Hangers for shafting, mixture for, 
281. 

Hardness, control of, 324-28. 

Hardware, light, mixture for, 281. 

Hatfield, W. H., experiment on de- 
flection with six bars, 384; in 
breaking bars, 387-88. 

Heat, measurement of, 206-10; radi- 
ation of, 208; resistance to, 335- 
38. _ 

Heat unit defined, 45. 

Heat-resisting iron, mixture for, 281. 

Heating and ventilating, 579-86. 

Height corresponding to acquired 
velocity, 193. 

Hemisphere, hollow iron, formula for 
finding weight of a, 571. 

Hexagon, relations of inscribed, to 
circle, 20. 

Hoisting rope, pliable wire, 179. 

Hollow ware, qualities of iron for, 
275; mixture for, 282. 

Hooks, slings and chains, 502-3. 

Hooper, G. K., on continuous melt- 
ing, 554-55- 



Index 



669 



Horse power defined, 45; required to 

compress air, 217—18. 
Housings for rolling' mills, mixture 

for, 282. 
Hydraulic cylinders, mixtures for, 

282. 
Hydraulic pressures, formulas for 

dimensions of cast iron pipe to 

withstand, 232-33. 
Hydrofluoric acid used for pickling, 

568. 
Hyperbola, the, 23-24. 

Inch, -one, decimal equivalents of 

parts of, 6. 
Inches to decimals of a foot, 6. 
Inclined plane, 194. 
Information, useful, 234-39. 
Ingot mould iron test bars, moduli of 

rupture of, 299. 
Ingot moulds and stools, mixture for, 

282. 
Iron and carbon, forms of combi- 
nation of, 313. 
Iron, band and hoop, weights per 

lineal foot, 121-22. 
Iron, burnt, of no use except for sash 

weights, 293. 
Iron castings, formulas for finding 

weight of, 570^75- 
Iron, flat, weight of, per foot, 45. 
Iron, flat plates, weight of, per square 

foot, 45. 
Iron, flat rolled, weights of, per lineal 

foot, 123-28; a:reas of, 129. 
Iron, mixing, by fracture, 273-74; by 
analysis, 274-89; mixtures for 
various classes of castings (al- 
phabetical), 276-87. 
Iron ores, varieties of, 240. 
Iron, physical properties of, 241. 
Iron, pig, see, Pig iron. 
Iron roofing, corrugated, weight of, 

141. 
Iron, round, weight of, per foot, 45. 
Iron, sheet, gauges used by U. S. 
mills in rolling, 120; weight per 
foot, 141. 
Iron, temperatures of, corresponding 

to various colors, 239. 
Iron wire, gauges and weights of, 146; 
list prices of, 147. 



Iron, wrought, weight and areas of 
square and round bars, 136-39. 

Jigs, by S. H. Stupakoff, 540-46. 
Jobbing castings, general, average of 

five meltings, 455. 
Jobbing castings, light, average of four 

meltings, 455. 
Joule's equivalent, 207. 

Keep, W. J., on pig iron cast in iron 
moulds and in sand, 249-50; in- 
fluence of silicon on cast iron, 
259-60; injurious influence of 
sulphur, 263; effect of manga- 
nese, 266; on recovery of shot 
iron, 292; shrinkage of test bars, 
371-72; shrinkage chart, 372-74; 
strength table, 375; process of 
making coke, 426. 

Kent, William, altitudes correspond- 
ing to barometric readings, 217; 
head in feet of water corre- 
sponding to pressure, 219; pres- 
sure for different heads, 219. 

Kettles to stand red heat, mixture 
for, 274. 

Ladles and table of capacities, 462-65. 

Lag screws, 158. 

Land measure, table of, 37. 

Le Chatelier, M., on furnace tem- 
peratures, 206. 

Lead pipes, sizes and weights of, 171. 

Ledebur, Prof. A., influence of silicon 
on annealing temperature, 391. 

Lees, Ernest J., areas and weights of 
fillets of steel, cast iron and brass, 
145- 

Lever, the, 194. 

Lifting beams, 503-5; table of safe 
loads for, 504. 

Lighting, importance, 578-79. 

Lime mortar, tensile strength of, 215. 

Liquid and dry measures, British Im- 
perial, weights of, 39-40. 

Liquid measure, table of U. S., 38; 
weights of volumes of distilled 
water, 39-40. 

Liquid pressure on moulds, 529-30. 

Locks and hinges, see Hardware, light. 

Locomotive castings, mixtures for, 282, 



670 



Index 



Locomotive cylinders, mixtures for, 
273, 282; specifications for, 355. 

Long measure, table of, 36; miscel- 
laneous, 37. 

Longmuir, Percy, on the sulphur con- 
tent of cast iron, 261-62; micro- 
structure of cast iron, 345-49; 
on sihcon in malleable castings, 
386; on steels, 394. 

Loudon, A. M., comparative values 
of core binders, 481-86. 

Lumber, weight of, per 1000 feet 
board measure, 93. 

McGahey, C. B., tests of use of steel 
scrap in mixtures of cast iron, 291. 

Machine-cast pig iron, see Pig iron, 
248-50. 

Machinery castings, heavy, average 
of four meltings, 457. 

Machinery castings, light, average of 
six meltings, 456. 

Machinery castings, qualities of iron 
for, 275; mixtures for, 283. 

Machinery iron test bars, moduli of 
rupture of, 299, 300. 

McWilliams & Longmuir on malleable 
castings, 382; on annealing, 400- 
i; on moulding machines, 548. 

Magnesite, bricks of, 436. 

Malleable cast iron, 382-93: Black 
heart, 382-85; experiments on 
varying compositions of, 383-84; 
ordinary or Reaumur, 385-88; 
mixtures in American practice, 
389-91; specifications and tests, 
391-93- 

Manganese, per cent, 308, 310, 315; 
high, 322; for elasticity, 323; as 
hardening agent, 324-25; in 
chilled iron, 328, 337; effect on 
grain structure, 329; increases 
shrinkage, 332; little effect on 
melting point, 334; for heat re- 
sistance, 337; low for permeabil- 
ity, 340; for acid resistance, 341; 
for resistance to wear, 342; skin 
effects, 344; in micrographs, 346- 
48; determination of, 379. 

Manganese, properties of, 265; in- 
fluence of, as constituent of cast 
iron, 265-66, 272. 



Mann, W. I., lengths of chords for 
spacing circle whose diameter is 
i» 90- 

Martensite "beta" form of iron, 313. 

Mayer, Dr. A. M., on radiation of 
heat, 208. 

Measures, miscellaneous, 39; and 
weights, 44. 

Measures of work, power and duty, 
45- 

Measures, see Weights and measures; 
also name of measure, as Dry 
measure. Liquid measure, etc. 

Mechanical analysis of cast iron, 371- 
77; Keep's shrinkage chart, 372- 
74; strength table, 375. 

Mechanical equivalent of heat, 207. 

Melting, continuous, 551-55. 

Melting losses in cupolas, tables of, 
454-61. 

Melting ratio, 461. 

Mensuration, 26-34. 

Metalloids, influence of the more im- 
portant, on combined carbon, 
272; method of adding, to the 
iron, 465. 

Metals, conductivity of, 206, 209; 
weights per cubic inch of, 239. 

Metals, sheet, Birmingham gauge for, 
except steel and iron, 120; 
weights of, per square foot, 142. 

Metric measures and weights in U. S. 
standard, 40-43. 

Micrographs of graphite, 308-11. 

Micro-structure of cast iron by P. 
Longmuir, 345-49- 

Mixing machines in core room, 497. 

Modulus of elasticity, 181-83. 

Modulus of rupture, 185-86; for- 
mula for, 304; in pounds per 
square inch, 298-303. 

Moldenke, Dr. R., effects of titanium 
and vanadium in cast iron, 2 68-70; 
on fusibility of cast iron, 332-33.; 
contents of malleable cast iron, 
389; specifications for foundry 
coke, 428-29. 

Molten iron, formulas to find pres- 
sure of, 575. 

Moment of inertia, 187; of rotating 
body, 197. 

Moments, location of, 180. 



Index 



671 



Monomial, 10. 

Mortar, lime and cement, tensile 
strength of, 215. 

Motor frames, see Dynamo. 

Mould, pressure on, by molten metal, 
formula to find, 575. 

Moulding, dry sand, mixtures for 
(West), 477-78. 

Moulding machines, 538-50: Jigs by 
S. H. Stupakoff, 540-46; flasks, 
547-50; diagram of moulding 
operations, 549. 

Moulding operations, diagram of 
(Stupakoff), 549. 

Moulding room and fixtures, 501-37: 
Cranes, 502; hooks, slings and 
chains, 502-3; lifting beams, 
503-5; binder bars, 505; clamps, 
506; flasks, 506-19; pins, plates 
and hinges, 519-21; sweeps, 522- 
23; anchors, gaggers, and sol- 
diers, 523—24; sprues, risers and 
gates, 524-27; tables of areas of 
gates, 525; strainers and spindles, 
528; weights, 528; chaplets, 528- 
37; liquid pressure on moulds, 
529-30; sprue cutters, 537. 

Moulding sand, 468-91: Cohesion, 
468; permeability and porosity, 
468-69; refractoriness, 469; du- 
rability, 469; texture, 469, 471; 
grades of various, 470; analysis, 
471 ; sand for brass, with analysis, 
472; test bars of green sand, 
473-76; for dry sand moulding, 
477-79; skin drying, 479; core 
sand, and analyses, 479-80; 
core mixtures, 480-86; parting 
sand, 486; facings, 486-87; 
graphite facing, 488; analyses, 
488-91. 

Moulds, multiple, 555-58; perma- 
nent, 558-61; mixtures for per- 
manent, 283. 

Multiphcation in algebra, 8-10. 

Nagle, F. A., on erratic results of in- 
vestigation of test bars, 298, 301- 
_ 3- 

Nails, common wire, 148. 

Nails, force required to pull, from 
various woods, 238. 



Nickel, properties of, 267; effect of, 
in cast iron, 267; imparts most 
valuable properties to steel, 267. 

Niter pots, see Acid-resisting. 

Nitrogen, properties of, 271; effect 
of, on cast iron and steel, 271. 

Nonconductivity of materials, 209-10. 

Novelty iron test bars, moduli of rup- 
ture of, 300. 

Nuts and bolt heads, weights of, 159. 

Nuts and washers, number of, to the 
pound, 152. 

Open-hearth methods for steel castings 
by W. M. Carr, 411-16. 

Ordway, Prof., on non-conductivity, 
209. 

Ornamental work, mixture for, 283. 

Outerbridge, A. E., tests of moulding 
sands, 473-75- 

Oxygen, effect of dissolved oxide on 
cast iron, 315, 318, 319, 320. 

Oxygen, properties of, 270; causes 
foundryman much trouble, 270- 
71; effective deoxidizers, 271. 

Parabola, the, 22-23. 

Parallelogram, area of, 26. 

Parenthesis, in algebra, 10, 

Parting sand, 486. 

Pattern lumber, specific gravity and 
weight per cubic foot of, 569. 

Pattern plates, preparation of, 540-46. 

Patterns for test bars of cast iron, 297. 

Pearlite, a mixture of fernite and 
cementite, 241, 347. 

Pentagon, to construct a, 20. 

Percentage, 5-7. 

Permeability and porosity of moulding 
sand, 468-69. 

Permeabihty, importance of, 339-40. 

Phosphorus, properties of, 263; in- 
fluence of, as constituent of cast 
iron, 264, 272; per cent, 308, 320- 
21; in micrographs, 309-11; low, 
for strong castings, 321; and for 
elasticity, 323; slight hardenmg 
effect, 324; slight influence on 
chill, 328; decreases shrinkage, 
332; increases fusibihty, 332-33, 
336; keep high for fluidity, 334- 
35; low for wear resistance, 342; 



672 



Index 



presence in micrographs, 346-49; 
determination of, 378. 

Physical constants, tables of, 202-3. 

Piano plates, mixture for, 283. 

PickUng, 567-68. 

Pig iron, physical properties of, 241- 
42; grading, 242-43; foundry, 
244-48; machine-cast, 248-50; 
charcoal iron, 250; grading scrap 
iron, 250-51; fracture of, index 
of composition, 273. 

Pig iron directory, 633-59: Coke and 
anthracite irons, 635-55; char- 
coal irons, 655-59- 

Pillow blocks, mixture for, 284. 

Pins, plates and hinges, 519-21. 

Pipe and pipe fittings, mixtures for, 
284. 

Pipe, cast-iron, specifications for, 356- 
63; tables of dimensions, 358 
of thicknesses and weights, 359 
volume and weight, 364-65 
pattern, size and weight, 366-70. 

Pipes, contents of, 102-3. 

Piston rings, mixture for, 284. 

Plane figure, irregular, area of any, 27- 
28. 

Plane figures, properties of, 24-26. 

Plane surfaces, mensuration of, 26-29. 

Plow points, chilled, mixture for, 284. 

Polygon, area of a, 27. 

Polyhedra, 31-32. 

Polynomials, lo-ii. 

Porter, Prof. J. J., effects of sulphur 
on cast iron, 262-63; of phos- 
phorus, 264; influence of the 
metalloids on combined carbon, 
272; report on mixtures for 
various classes of castings (al- 
phabetical), 276-87; on proper- 
ties and mixtures of cast iron, 
312-14; pig iron classification 
and directory, 633-59. 

Pouring temperature, influence of, 
318. 

Powers of quantities, 9-10. 

Prince, W. F., process for melting 
borings, 293. 

Printing presses, see Machinery cast- 
ing. 

Prism, the, 30. 

Prismoid, the, 31. 



Probert, Richard H., analysis of iron 
for permanent moulds, 558-59. 

Propeller wheels, mixture for, 284. 

Proportion, 1-2. 

Pulleys, circumferential speed of, 229- 
30; rules for speeds and diameters 
of, 231; mixtures for, 274, 284- 
85. 

Pumps, hand, mixture for, 285. 

Pyramid, the, 30-31. 

Quadratic equations, solution of, 14- 

15- 

Quadrilateral, area of any, 27. 

Quantities, in algebra, 7-10: addition 
of like and unlike, 8; multi- 
phcation of simple and com- 
pound, 9. 

Radiation of heat, 208. 
Radiators, mixture for, 285. 
Railroad castings, mixture for, 285; 

average of three meltings, 459. 
Rake, cupola, 467. 
Ratio, 1-2. 
Reaumur malleable cast iron, 385-88: 

Remelting, 385-86; annealing, 

386; analyses, 387-88. 
Retorts, See Heat resisting castings. 
Richards, horsepower required for air 

compression and delivery, 217-18. 
Ries, Prof. H., analyses of moulding 

sands, 472-73. 
Rings, cast iron, formulas to find 

weight of, 574. 
Rivets, iron, round head, 166. 
Rolling mill rolls, mixture for, 274. 
Rolls, chilled, mixtures for, 274, 275, 

285. 
Roofing, corrugated iron, weight of, 

141. 
Roofing, tin and other, 169-70. 
Root Positive Rotary Blowers, 449. 
Roots of numbers, 3-5. 
Rossi, G. A., on effect of titanium in 

cast iron, 268. 
Rupture, modulus of, 185-86; for- 
mula for, 304. 

Sand blast, the, 566. 

Sand bottom of cupola, 441. 

Sand conveyors and driers, 497, 498. 



Index 



673 



Sand, rammed, to find weight of, 572. 

Sand roll iron test bars, moduli of 
rupture of, 299. 

Sanitary ware, qualities of iron for, 
27s; average of eight meltings, 
■4S8. 

Sash weight, mixture for, 274, 275. 

Sash weight iron test bars, moduli of 
rupture of, 299. 

Scales, mixture for, 2S5. 

Scott, W. G., influence of the chemi- 
cal constituents of cast iron, 252. 

Scott, W. G., specifications for coke, 
426; for moulding sand, 472; 
analyses of core sands, 479-89; an- 
alysis of Yougheogheney gas coal, 
487; analyses of graphite, coke 
dust, coal and charcoal, 488-91. 

Scott, W. G., specifications for graded 
pig irons, 243. 

Scrap iron, grading, 250-51. 

Secant, the, 108. 

Set screws, steel, list price per 100, 169. 

Shafting, See Steel shafting. 

Sheath, Mr., on continuous melting, 

55 1-54- 
Sheet brass and all metals except steel 
and iron, Birmingham gauge for, 
120. 

Sheet iron. See Iron, sheet. 

Sheet metals, weights of, per square 
foot, 142. 

Shot iron, recovering and melting, 
291-93. 

Shrinkage chart, by W. J. Keep, 372- 
374- • 

Shrinkage of castings per foot, 234. 

Shrinkage or contraction, 329-32. 

Signs and abbreviations, v. 

Silica brick, analysis of, 435. 

Silicon, per cent, 308, 310; should be 
low, 315, 321; for elasticity, 323; 
for hardness, 325; for chill, 327; 
decreases shrinkage, 332; little 
effect on fusibility, 334; aids 
fl.uidity, 334; favors growth by 
repeated heating, 337; increases 
permeability, 340; increases acid 
resistance, 341; decreases resist- 
ance to wear, 342; unrecognizable 
in micrographs, 346; determina- 
tion of, 377-78. 



Silicon, properties of, 256; influence of 

as a constituent of cast iron, 256- 

60, 272. 
Sines, natural, tangents and secants, 

107-8; tables of, 1 10-14. 
Skin drying moulds, 479. 
Slag car castings, mixture for, 285. 
Slags, comparison of analyses of, 432- 

33- 
Smoke stacks, locomotive. See Loco- 
motive castings. 
Soil pipe and fittings, mixture for, 

286. 
Soldiers, 524. 

Solids, and their mensuration, 30-34. 
Solids, center of gravity of, 196-97; 

lineal expansion for, 205. 
Specific gravity of various substances, 

197-201. 
Specifications for steel castings, stand- 
ard, 409-11. 
Speeds, grinding wheel, 231. 
Speeds, surface, rules for obtaining, 

232. 
Sphere, the, 33-34- 
Sphere, hollow iron, formula forjfind- 

ing weight of a, 572; of a solid 

iron, 571. 
Spheres, table of surface and volumes 

of, 93-98. 
Spherical segments, cast iron, for- 
mulas to find weight of, 573. 
Spill bed, 466. 
Sprocket wheels for ordinary link 

chains, 176-78. 
Sprue cutters, steel, 537. 
Square measure, tables of, 37-38. 
Square of a whole number ending with 

ciphers, to find, 56. 
Square root, 3-4. 
Square root of large number not in 

table, to find, 62. 
Square roots of numbers from 1000 to 

10,000, 57-61. 
Squares and square roots of numbers, 

of from .01 to 1000, tables of, 

46-56. 
Stead, J. E., on relations of iron and 

phosphorus, 348. 
Steam chests. See Locomotive and 

Machinery castings. 
Steam cylinders, mixtures for, 286. 



674 



Index 



Steel castings in the foundry, 394-416: 
Content of carbon in varieties, 
394~95J mechanical properties 
"Normal steels," 396; Bessemer 
process, 396; Baby converter 
(Robert), 397; gases in, 398; 
chemical changes in Tropenas 
converter, 397-99; annealing, 
with micrographs, 400-1 ; Trope- 
nas process, 401-3; chemistry of 
the process, 403-4; converter 
linings, 404-5 ; converter practice, 
406-9; standard specifications, 
409-11; open-hearth methods by 
W. M. Carr, 411-16. 

Steel, comparative cost of, made by 
different processes (B.Stoughton), 
417-24: Acid open hearth, 417, 
419, 422; basic open hearth, 418, 
419, 423; converter, 420, 421; 
crucible castings, 423; electric 
furnace, 424. 

Steel, fillets of, areas and weights of, 

I4S- 

Steel, flat rolled, weights of, per lineal 
foot, 130-35- 

Steel scrap, use of, in mixtures of 
cast iron, 290-91; points to be 
watched in melting, 316-17; 
closes the grain, 319; per cent of, 
322. 

Steel shafting, cold rolled, weights and 
areas of, 140. 

Steels, mechanical properties of "nor- 
mal, " 396. 

Steels, unsaturated and supersatu- 
rated, 241. 

Stoughton, Bradley, tables of com- 
parative cost of steel made by 
different processes, 417-21. 

Stove plate, qualities of iron for, 275; 
mixture for, 286; average of 
three meltings, 457. 

Stove-plate iron test bars, moduli of 
rupture of, 300. 

Straight line, problems of the, 15-17. 

Strainers and spindles, 528. 

Straw rope for core bodies, 499. 

Strength of beams, transverse, for- 
mulas for, 188-90. 

Strength of cast iron, nine factors 
which influence, 315-22. 



Strength of materials, 185-86, 213-14. 

Strength table by W. J. Keep, 375. 

Strengths, transverse, table of, 1S5-86. 

Stupakoff, S. H. Chapter on jigs, 
540-46. 

Sturtevant Steel Pressure Blower, 448. 

Subtraction in algebra, 8. 

Sulphur, properties of, 260; deleteri- 
ous influence of, in cast iron, 261- 
63, 272; per cent, 308, 315, 321; 
low for elasticity, 323; harden- 
ing effect of, 325; increases com- 
bined carbon, 327-28; effect on 
shrinkage, 332; on melting point, 
334. 336; low for heat resistance, 
337; and for corrosion resistance, 
339-42; increases resistance to 
wear, 342; causes dirty castings, 
343; in micro-structure, 346-48; 
determination of, 378. 

Sulphuric acid, use of, in pickling, 
567-68. 

Sweeps, 522-23. 

Tacks, length and number of, to 
pound, 148. 

Tangent, 107. 

Tanks, rectangular, capacity of, in 
U. S. gallons, 99-100; number of 
barrels in, loo-i. 

Tapers per foot and corresponding 
angles, table of, 1 17-18. 

Tapping bar,. 463. 

Taylor and White, temperatures cor- 
responding to various colors of 
heated iron, 239. 

Temperatures, equivalent. Centigrade 
to Fahrenheit, 211-12. 

Temperatures, furnace, 206. 

Tensile Strength, ratio of, to breaking 
loads, 10 to I, 302; D. K. 
Clarke's formula for, 304. 

Tensile test, size of bar for, 295-97. 

Test bars, report on by committee of 
American Foundrymen's Asso- 
ciation, 294-306: Character of 
the heats, 294; making of cou- 
pons, 295; specifications for gray 
iron castings, i296-97; patterns 
for, 297; moduli of rupture, 298- 
300; erratic results, 298, 301-2; 
comparison of, 302-3; casting 



Index 



67s 



defects, 304; circular, 304-6; 
microscopical evidence why simi- 
lar irons have different relative 
strengths, 306-12; Prof. Porter 
on the physical properties of cast 
iron, 312-14. 

Thermit, use of, in the foundry, 270. 

Thermometer scales, comparison of, 
213. 

Threads, U. S. standard, 149. 

Thumb screws, 165. 

Tin and copper, alloys of, 222. 

Tin, copper and zinc, alloys of, 224-25. 

Tin, roofing, 169-70. 

Tin, sheet, sizes and weight of, 142. 

Titanium, properties of, 267; effect 
of, in cast iron, 267-68. 

Tobin bronze, 225. 

Tons, gross, in pounds, 235. 

Transverse strength, See Strength. 

Transverse test, size of bar for, 295- 
98; See Test bars. 

Trapezium, area of a, 27. 

Trapezoid, area of a, 27. 

Triangle, area of a, 26. 

Triangle, right-angled, solution of, 
109. 

Triangles, obUque-angled, solution of, 
109. 

Tropenas converter, chemical changes 
in a, 397. 

Tropenas process of steel making, 
401-3; chemistry of the process, 

405-4- 

Troy weight, table of, 36. 

Tubes, brass and copper, seamless, 
167-69. 

Tumblers and tumbUng mills, 563-66. 

Turn-buckles, drop-forged, 162-63. 

Turner, Prof.- T., on varieties of pig 
iron, 253; percentages of com- 
bined carbon, 256; on the use 
of silicon, 257-59; phosphorus 
in cast iron, 264. 

Tuyeres, construction of, in cupola, 
439-40. 

Two-foot rule, measurement of angles 
with, 1 1 5-1 6. 

Unit of heat, 207. 

Units, electrical and mechanical, 
equivalent values of, 220-21. 



Valves, mixtures for, 286. 

Vanadium, properties of, 268; Mol- 
denke's experiments on action of, 
on cast iron, 269-70. 

Ventilating, See Heating and venti- 
lating. 

Walker, F. G., shrinkage of castings 
per foot, 234; weight of castings 
determined from weight of pat- 
terns, table, 570. 

Washer, lock, 153; positive lock, 
154- 

Washers, wrought steel plate, 153. 

Water, distilled, weights of volumes 
of, 39-40. 

Water heaters, mixtures for, 286. 

Water, pressure of, 219. 

Water supply, 577-78. 

Watts in terms of horse power, 45, 

Wear, resistance to, 342. 

Weaving machinery, See Machinery 
castings. 

Wedge, the, 31, 195. 

Weight of castings determined from 
weight of patterns, 569-70; for- 
mulas for finding, 570-76. 

Weights, 528. 

Weights and measures, 35-^45; tables 
of various, 46—106. 

Wells, contents of linings of, 104-6. 

West, Thomas D., on power of cast 
iron to stretch, 332. 

Wheel and axle, 194. 

Wheels, mixtures for, 287. 

Whitehouse, J. S., on side blow con- 
verters, 404-8. 

Willson, E. M., table of tapers per 
foot and corresponding angles, 
1 1 7-1 8. 

Wind box of the cupola, 445-46. 

Window glass, panes of, in a box, 
236. 

Wine measure, table of, 38. 

Wire, brass. See Brass. 

Wire, copper. See Copper. 

Wire, coppered Bessemer spring, 
147. 

Wire, coppered market, 147. 

Wire gauges, different standards for, 
119-20. 



676 Index 

Wire, iron, gauges and weights of, 146; Wrought Iron, See Iron, wrought. 

list prices of, 147. 

Wood working machinery. See Ma- Zinc and copper, alloys of, 223. 

chinery castings. Zinc, copper and tin, alloys of, 224-25. 

Wrot pipe, dimensions of standard, Zones in cupola, 437, 442—43. 

167-69. 



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